Math Profile 2016 New - IISER Pune Profile 2016.pdfSneha#Jondhale# Soumen#Maity# Soumyadip#Thandar#...

Mathematics**at#IISER#Pune#

!2016%IISER%Pune%Math%Book%

Abhinav#Sahani#Abhishek#Kumar#Shukla#Advait#Phanse#Aman#Jhinga#Amit#Hogadi#Anindya#Goswami#Anisa#Chorwadwala#Anup#Biswas#Anupam#Singh#K#Arun#Kumar#Ayan#Mahalanobis##Ayesha#Fatima#Baskar#Balasubramanyam##

Bhagyalaxmi#Chaitanya#Ambi##Chandrasheel#Bhagwat#

Chitrabhanu#Chaudhuri##Debangana#Mukherjee##Debaprasanna#Kar#Debargha#Banerjee##Diganta#Borah##Dipramit#Majumdar##Girish#Kulkarni#Gunja#Sachdeva##Hitesh#Raundal##Jyotirmoy#Ganguly##Kalpesh#Pednekar##Kaneenika#Sinha##Krishna#Kaipa##Krishna#Kishore#Makarand#Sarnobat##Manidipa#Pal#Milan#Kumar#Das##

Math#Members#

Mousumi#Bhakta#Neeraj#Deshmukh##Neha#Malik#Neha#Prabhu##Pallavi#Kharade#Prabhat#Kushwaha##Pralhad#Shinde##Pranay#Goel##Rabeya#Basu#A#Raghuram#Rama#Mishra#Rashmi#Kulkarni#Rohit#Joshi#Ronnie#Sebastian##Safeer#K#M#Sameer#Kulkarni#Shane#D’Mello#

Sneha#Jondhale#Soumen#Maity#Soumyadip#Thandar#Steven#Spallone##Sucheta#Dawn#Sudhir#Pujahari##Suprita#Talnikar#Supriya#Pisolkar##Sushil#Bhunia##Suvarna#Gharat##Tathagata#Mandal##Tejas#Kalelkar#Uttara#NaikMNimbalkar##Vivek#Mallick##Yasmeen#Akhtar#

Compiling,*Editing*and*Design:*Supriya#Pisolkar#and#Shanti#Kalipatnapu#Cover*Page:*Bust#of#mathematician#HarishMChandra#created#by#Charlotte#Langlands#to#be#inaugurated#during#2016#Math#day#celebration#Photo*Courtesy:*IISER#Pune#Math#Members##


I#have#now#completed#four#years#as#Coordinator#for#Mathematics#at#IISER#Pune,#and#furthermore,#IISER#Pune#turns#10#

this#year.#This#seems#like#an#opportune#moment#to#stop#and#reflect#on#what#has#been#achieved#so#far,#and#where#we#

have#scope#for#development.##

We#are#now#about#65#people#in#Mathematics#including#faculty,#postdocs,#PhD#and#Integrated#PhD#students,#5th#year#

BS#MS#students,#teaching#and#project#assistants,#and#staff.#This#signifies#a#very#healthy#growth,#and#our#numbers#have#

more# than# tripled# in# the# last# five# years.# However,# the# rate# of# growth# has# certainly# come# down,# but# we# are# at# an#

enviable# position# of# choosing# amongst# the# best# to# join# us.# I# am# especially# proud# of# the# growth# of# our# postdoc#

program.#We#are#getting#very#highMquality#applications#from#PhD#programs#around#the#world.#With#some#luck,#by#Fall#

2016,# we#might# have# around# 7# postdocs# in#Mathematics.#We# have# had# continuing# success# in# our# BS#MS# students#

getting# placed# in# excellent# PhD# programs;# let# me# mention# Shiva# Chidambaram# is# now# studying# at# University# of#

Chicago,#and#Nishad#Mandlik#who#is#at#Oklahoma#State#University.##

In# the# year# 2015M2016,#we#were# selected# for# a# grant# under# the# FIST# program# that# gives# us# about# 1.5# Cr# for# a# high#

performance#computer# cluster,# a# computer# lab,#and# some# funds# to# supplement#our# library.#This#bodes#well# for#our#

program#and#for#its#visibility#on#the#national#science#scene.##

IISER# Pune# has# been# publishing# in# some# topMtier# journals#

such#as# the#American*Journal*of*Mathematics,#Advances*of*

Mathematics,# Annals* of* Applied* Probability# etc.# However,#

on# this# note,# I# feel# that# we# are# not# yet# an# international#

force# to# reckon# with.# We# have# a# long# way# to# go# in#

increasing# both# the# quality# and# quantity# of# papers# in#

Mathematics.##

I# had# a# personal# success# in# getting# elected# as# a# Fellow#of#

the#Indian#Academy#of#Sciences.#But#this#goes#beyond#my#

personal#self,#as#it#is#important#in#administrative#circles#for#

the# leader# of# a# program# to# be# decorated# by# national# or#

international# recognitions.# It# adds# to# the# sheen# of# the#

program# and# helps# to# garner# future# grants# and#

recognitions#for#the#scholars#of#that#program.#Success,#as#a#

wise#man#once#said,#begets#success.##

All#in#all,#IISER#Pune#is#doing#well#and#has#positioned#itself#

to#be#an#important#center#for#Mathematics#in#India.#It#is#my#

hope# that# we# make# it# into# a# place# to# be# well# known# in#

international# circles# as# the# place# that# proves# great#

theorems!##

Welcome*Message*

A.#Raghuram#Coordinator,#Mathematics,#IISER#Pune#


Algebraic*Geometry*

One#can#describe#algebraic#geometry#as#the#study#of#varieties,#which#are#spaces#defined#by#vanishing#of#polynomial#equations.#I#have#been#interested#in#moduli#spaces#which#are#special#types#of#varieties#which#parametrize#geometric#objects.##In#the#last#couple#of#decades,#people#have#succeeded#in#applying#ideas#from#topology,#especially#homotopy#theory,#to#the#study#of#algebraic#varieties.#This#interplay#between#homotopy#theory#and#algebraic#geometry#has#been#one#of#my#latest#fascinations.##Currently,# I# am# working# on# problems# which# are# sometimes# clubbed# under# the# title#homotopical# algebraic# geometry# and# have# applications# to# KMtheory,# motivic#cohomology#and#also#classical#topics#like#Brauer#groups.##Selected#Publications#With# Indranil# Biswas.# Fundamental# group# of# quotient# singularities.# To# appear# in# International*Mathematics*

Research*Notices.#

Esnault,#H.#and#Hogadi,#A.# (2012).#On#the#algebraic#fundamental#group#of#smooth#varieties# in#characteristic#

p>0.#Transactions*of*the*American*Mathematical*Society#364:2429M2442.#

Hogadi,#A.#and#Mehta,#V.#(2011).#Birational#invariance#of#the#SMfundamental#group#scheme.#Pure*and*Applied*

Mathematical*Quarterly#7(4):1361M1370.#

Hogadi,#A.#and#Pisolkar,#P.#(2011).#On#the#cohomology#of#Witt#vectors#of#pMadic#integers#and#a#conjecture#of#

Hesselholt.#Journal*of*Number*Theory#131(10):1797M1807.#

Hogadi,#A.#and#Xu,#C.# (2009).#Degenerations#of# rationally# connected#varieties.#Transactions*of* the*American*

Mathematical*Society#361(7):3931M3394.##

Amit*Hogadi*Associate#Professor#[email protected]###Amit#Hogadi#received#PhD#from#Princeton#University,#USA#in#2007.#He#was#at#Tata#Institute#of#Fundamental#Research#(TIFR),#Mumbai,#India#before#joining#IISER#Pune#in#December#2013.#

#


Stochastic*Control*–**Game*Theory,*Math*Finance,*Queuing*

Networks,*Renewal*Processes!

I# am# exploring# various# topics# in# Applied# Probability.# Those# include# generalization# of#BlackMSholesMMerton# PDE# for# options# in# semiMMarkov# modulated# market,# Föllmer#Schweizer# decomposition# of# an# unattainable# contingent# claim,# equilibrium# of# nonMcooperative#semiMMarkov#game#under#ergodic#cost,#optimal#control#under#risk#sensitive#cost,# portfolio# optimization,# large# deviation# limit,# fluid# limit# in# queuing# network,# PDE#techniques#in#stochastic#control#and#differential#games#etc.##I#use#Markov#models,#filtering#techniques,#stochastic#calculus,#infinitesimal#generator#for#semigroup# of# operators,# mild# solution# technique# for# parabolic# equations,# viscosity#solution# method# for# HJB/HJI# equations,# stability# analysis# of# numerical# schemes# for#solving#PDE#or#IE,#convergence#of#value#iteration#schemes,#marginalization#technique#in#rare#event#simulation#for#hybrid#processes,#martingale#formulation#for#Markov#processes#etc.#

#Selected#Publications#Goswami,#A.# and#Nandan,# S.# (2016).# Convergence# of# estimated# option# price# in# a# regime# switching#market.#

Indian*Journal*of*Pure*and*Applied*Mathematics#(to#appear)#

Goswami,#A.#and#Saini,#R.K.#(2014).#Volterra#equation#for#pricing#and#hedging#in#a#regime#switching#market.#

Cogent*Economics*&*Finance#1(2):1M11.#

Atar,#R.,#Goswami,#A.#and#Shwartz,#A.#(2014).#On#the#riskMsensitive#cost#for#a#Markovian#multiclass#queue#with#

priority.#Electronic*Communications*in*Probability#19(11):1M13.#

Atar,#R.,#Goswami,#A.#and#Shwartz,#A.#(2013).#RiskMsensitive#control#for#the#parallel#server#model.#SIAM*Journal*

on*Control*and*Optimization#51:4363M4386.#

Basak,#G.K.,#Ghosh,#M.K.#and#Goswami,#A.#(2011).#Risk#minimizing#option#pricing#for#a#class#of#exotic#options#

in#a#Markov#modulated#market.#Stochastic*Analysis*and*Applications#29:259M281.#

Ghosh,#M.K.,# Goswami,# A.# and# Kumar,# S.K.# (2010).# Portfolio# optimization# in# a#Markov#modulated#market:#

Chapter# in#Modern#Trends# In#Controlled#Stochastic#Processes:#Theory#and#Applications.#Luniver#Press,#

pp.#181M195.#

Ghosh,# M.K.,# Goswami,# A.# and# Kumar,# S.K.# (2009).# Portfolio# optimization# in# a# semiMMarkov# modulated#

market.#Applied*Mathematics*&*Optimization#60:275M296.##

Ghosh,#M.K.# and#Goswami,#A.# (2009).# Risk#minimizing# option# pricing# in# a# semiMMarkov#modulated#market.#

SIAM*Journal*on*Control*and*Optimization#48:1519M1541.#Ghosh,#M.K.#and#Goswami,#A.#(2008).#Partially#observable#semiMMarkov#games#with#average#payoff.#Journal*of*

Mathematical*Analysis*and*Applications#345:26M39.#

Anindya*Goswami*Assistant#Professor#[email protected]###Anindya#Goswami#received#his#PhD#from#Indian#Institute#of#Science#(IISc),#Bangalore,#India#in#2008.#Following#this,#he#held#postdoctoral#positions#at#the#Universiteit#Twente#in#Enschede,#The#Netherlands;#INRIA#in#Rennes,#France;#and#Technion#in#Haifa,#Israel#before#joining#IISER#Pune#in#2011.#

#


Shape*Optimization*Problems!

My# research# work# falls# mainly# in# the# following# two# branches# of# Mathematics:# Partial#differential# equations# and# Riemannian# geometry.# I# work# on# shape# optimization#problems# including# isoperimetric#problems.#A#typical#shape#optimization#problem#is#to#find# a# shape#which# is# optimal# in# the# sense# that# it#minimizes# a# certain# cost# functional#while# satisfying# given# constraints.# In# many# cases,# the# functional# being# minimized#depends#on#the#solution#of#a#given#partial#differential#equation#defined#on#the#variable#domain.#

We# have# solved# some# shape# optimization# problems# for# a# class# of# doubly# connected#domains#over#RankMone#symmetric#spaces#of#nonMcompact#type.#Among#the#RankMone#symmetric#spaces#of#compact#type,#we#dealt#only#with#the#case#of#Sn,#the#unit#sphere#in#�n+1#with# the# induced#metric.# In# fact,#we# gave# a# uniform#proof# for# all# the# three# space#forms.# Here,# the# functionals# to# be# optimized# were# the# energy# functional# and# the#principal# frequency# associated# with# the# Dirichlet# boundary# value# problem# and# the#Dirichlet#Eigenvalue#problem#respectively,# for#both# linear#as#well#nonMlinear#operators,#namely#the#Laplacian#and#the#pMLaplacian.#

So#far#we#were#solving#the#shape#optimisation#problems#over#a#family#of#punctured#balls#where#the#puncture#was#also#spherical#and#was#free#to#move#in#the#interior#of#the#outer#ball.# We# are# now# considering# solving# a# shape# optimisation# problem# over# a# different#family# of# domains.# It# is# again# a# family# of# spherical# punctured# domains;# however,# this#time#the#puncture#is#not#spherical#but#has#other#symmetries#and#is#free#to#rotate#about#its#`center’.#We#are#also#trying#to#prove#analogous#results#in#the#area#of#Spectral#Graph#Theory.##

##

Selected#Publications#Anisa,#M.H.C.#and#Mahadevan,#R.#(2015).#An#eigenvalue#optimisation#problem#for#the#pMLaplacian.#Proceedings*

of*the*Royal*Society*of*Edinburgh:*Section*A*Mathematics#DOI:#10.1017/S0308210515000232#

Anisa,# M.H.C.,# Mahadevan,# R.# and# Toledo,# F.# (2015).# On# the# FaberMKrahn# inequality# for# the# Dirichlet# pM

Laplacian.#ESAIM:*Control,*Optimisation*and*Calculus*of*Variations#DOI:#10.1051/cocv/2014017#

Anisa,# M.H.C.# and# Vemuri,# M.K.# (2013).# Two# functionals# connected# to# the# Laplacian# in# a# class# of# doubly#

connected#domains#on#rank#one#symmetric#spaces#of#nonMcompact#type.#Geometriae*Dedicata#167(1):11M

21.#DOI:#10.1007/s10711M012M9800M7#

Anisa*M*H*Chorwadwala*Assistant#Professor#[email protected]###Anisa#Chorwadwala#received#her#PhD#from#University#of#Mumbai#in#2007.#Following#this,#she#held#postdoctoral#positions#at#the#Institute#of#Mathematical#Sciences#(IMSc),#Chennai;#Abdus#Salam#International#Centre#for#Theoretical#Physics#(ICTP),#Trieste,#Italy;#and#Tata#Institute#of#Fundamental#Research#(TIFR),#Mumbai.#She#has#been#on#the#faculty#of#IISER#Pune#since#April#2011.##############Moving#Plane#Method#for#a#punctured#ball#

on#the#unit#sphere##


Stochastic*Controls*and**Queuing*Theory*

My# broad# research# area# falls# under# Applied# Probability.# I# am# mainly# interested# in#stochastic#controls,# small#noise#diffusion,#asymptotics#of#queuing#networks#and#many#other#related#models.#

In# the# last# couple# of# years,# I# have# worked# on# problems# from# queuing# theory# that#involves# measureMvalued# process.# Such# processes# have# proven# powerful# in# modeling#queuing#networks#with#general# service#and# reneging#distributions.#Another# important#area#of#queuing#theory#is#scheduling#control#where#one#looks#for#a#policy#that#optimizes#certain#cost#associated#to#the#model.#I#also#work#on#such#control#problems.#

#Selected#Publications#

Arapostathis,# A.,# Biswas,# A.# and# Pang,# G.# (2015).# Ergodic# control# of# multiMclass# M/M/N+M# queues# in# the#

HalfinMWhitt#regime.#Annals*of*Applied*Probability*25(6):3511M3570.#

Atar,# R.,# Biswas,# A.# and# Kaspi,# H.# (2015).# Fluid# limits# of# G/G/# 1+G# queues# under# nonMpreemptive# EarliestM

DeadlineMFirst#discipline.#Mathematics*of*Operation*Research#40(3):683M702.#

Biswas,# A.# (2014).# RiskMsensitive# control# for# the#multiclass#manyMserver# queues# in# the#moderate# deviation#

regime.#Mathematics*of*Operation*Research#39(3):908M929.#

Atar,# R.# and# Biswas,# A.# (2014).# Control# of# the# multiclass# G/G/1# queue# in# the# moderate# deviation# regime.#

Annals*of*Applied*Probability#24(5).##

Anup*Biswas*Assistant#Professor#[email protected]###Anup#Biswas#received#his#PhD#from#TIFRMCentre#for#Applicable#Mathematics,#Bangalore,#India#in#2011.#He#held#postdoctoral#positions#at#Technion,#Israel,#and#University#of#Texas,##Austin,#USA#before#joining#IISER#Pune.#####

#


Conjugacy*Questions*and*Representation*Theory*of*

Groups*

Conjugacy#questions# in#group#theory#have#been#of# interest#for# its#connection#with#the#representation# theory# and# they# have# not# been# understood# very# well# for# Algebraic#Groups#over#arbitrary#field.#Usually#groups#are#difficult#objects#and#one#studies#them#via#their#representations#to#get#a#better#understanding.##

Let#G#(e.g.#GLn)#be#an#algebraic#group#defined#over#a#field#k.#We#denote#the#k#points#of#G#by#G(k)#(e.g.#GLn(k),#SLn(k)#etc.).#An#element#t#of#G(k)#is#said#to#be#real#if#it#is#conjugate#to#its#own#inverse#in#G(k).#I#have#been#concerned#with#finding#real#elements#in#algebraic#groups.# Very# interestingly# often# it# relates# to# finding# strongly# real# elements# (the#elements#which#are#product#of#two#involutions#in#G(k)).##

Apart#from#studying#structure#of#real#elements#in#Algebraic#Groups#over#k,#I#also#looked#at#many#examples#such#as#linear#groups,#orthogonal#groups,#symplectic#groups#and#the#groups#of# type#G2# to#get#better# understanding#of# the#problem.# Finding# real# elements#helps# in# the# understanding# of# real# characters# of# the# group# which# in# turn# give#information# about# those# complex# representations# of# the# group# which# are# either#orthogonal#or#symplectic.#

#Selected#Publications#Gates,#Z.,#Singh,#A.#and#Ryan#Vinroot,#C.#Strongly#real#classes#in#finite#Unitary#groups#of#odd#characteristic.#To#

appear#in#the#Journal*of*Group*Theory.#

Kulshrestha,#A.#and#Singh,#A.# (2011).#Real#elements#and#Schur# indices#of#a#group.#The*Mathematics*Student#

80:73M84.##

Gill,# N.# and# Singh,# A.# (2011).# Real# and# strongly# real# classes# in#PGLn(q)# and# quasiMsimple# covers# of#PSLn(q).#

Journal*of*Group*Theory#14:461M489.#

Gill,#N.#and#Singh,#A.#(2011).#Real#and#strongly#real#classes#in#SLn(q).#Journal*of*Group*Theory#14:437M459.###

Anupam*Kumar*Singh*Assistant#Professor#[email protected]###After#doing#MSc#(Mathematics)#from#Indian#Institute#of#Technology#(IIT)#Kanpur,#Anupam#Singh#worked#for#his#doctorate#at#Harish#Chandra#Research#Institute,#Allahabad#and#Indian#Statistical#Institute#(ISI),#Bangalore,#India#and#got#PhD#from#ISI#in#2007.#He#held#postdoctoral#positions#at#Tata#Institute#of#Fundamental#Research#(TIFR),#Mumbai#and#Institute#of#Mathematical#Sciences#(IMSc),#Chennai,#India#before#joining#the#faculty#of#IISER#Pune#in#2008.##

#


Public*Key*Cryptography*

I# work# at# the# intersection# of# pure# mathematics# (group# theory)# and# public# key#cryptography.#Cryptography,#especially#public#key#cryptography,# is# the#backbone#of#a#modern#society.#It#serves#us#with#the#required#tools#for#online#transactions#and#trading,#i.e.,#online#commerce.##My# research# aims# to# find# new# cryptograhic# primitives# and# to# build# secure# protocols#from# that.#We# look# for# groups# in#which# the#discrete# logarithm#problem# is# secure.#My#recent#work#has# shown# that# the#group#of#nonMsingular# circulant#matrices#over#a# finite#field# has# some# properties# that# make# them# attractive# over# the# discrete# logarithm#problem# on# a# finite# field.# This# new# finding# has# opened# a# new# avenue# in# research# of#public#key#cryptography.#

#Selected#Publications#Mahalanobis,#A.#The#ElGamal#cryptosystem#over#circulant#matrices#(Submitted).#

Mahalanobis,#A.#and#Shah,#J.#(2014).#A#new#guessMandMdetermine#attack#on#the#A5/1#stream#cipher.#Computer*

and*Information*Science#7(1):115M124.#

Mahalanobis,# A.# (2013).# Are#matrices# useful# in# publicMkey# cryptography?# International*Mathematical* Forum#

8(39):1939M1953.#

Mahalanobis,# A.# The# MOR# cryptosystem# and# extraMspecial# pMgroups.# # Proceedings# of# WCC# 2012,# Castro#

Urdiales,#Spain#July#9M13,#2012#&#To#appear#in#Journal*of*Discrete*Mathematics*and*Cryptography.#

Mahalanobis,# A.# (2013).# The# automorphism# group# of# the# group# of# unitriangular# matrices# over# a# field.#

International*Journal*of*Algebra#7(15):723M733.#

Mahalanobis,# A.# (2012).# A# simple# generalization# of# the# ElGamal# cryptosystem# to# nonMabelian# groups# II.#

Communications*in*Algebra#40:3583M3596.#

Mahalanobis,# A.# (2010).# The# discrete# logarithm# problem# in# the# group# of# nonMsingular# circulant# matrices.#

Groups*Complexity*Cryptology#2:83M89.##

Ayan*Mahalanobis*Assistant#Professor#[email protected]###Ayan#Mahalanobis#obtained#his#PhD#from#Florida#Atlantic#University,#Boca#Raton,#USA#in#2005.#He#was#a#Visiting#Assistant#Professor#at#the#Stevens#Institute#of#Technology,#New#Jersey,#USA#for#a#few#years#before#joining#IISER#Pune#in#2009.####


Modular*Forms*and**Galois*Representations*

My#research#interests#are#in#Number#Theory.#A#modular#form#is#essentially#a#function#defined# on# the# complex# upper# halfMplane# (everything# above# the# real# axis)# that#behaves# in# a# good#way# under# transformations# of# certain# 2x2#matrices#with# integer#entries.# The# expansion# at# infinity# of# such# a# function# gives# us# a# power# series#whose#coefficients# have# interesting# arithmetic# properties.# An# important# example# of#numbers# that# arise# in# such# a# way# is# the# Ramanujan# Tau# function# τ(n).# In# order# to#understand#these#coefficients,# it# is#useful# to#consider#an#object#attached#to# it#called#the#LMfunction#(these#are#generalizations#of#the#Riemann#zeta#function).#

A# Galois# group# is# a# set# of# permutations# of# roots# of# an# irreducible# polynomial.# For#example,#complex#conjugation#permutes#the#roots#of#x2+1.#It#is#possible#to#represent#such#permutations#by#matrices.#One#of#the#problems#in#Number#Theory#is#to#try#and#understand#the#Galois#group#by#studying#its#representations.#One#can#also#attach#LMfunctions# to# Galois# representations# and# in# some# cases# modular# forms# and# Galois#representations#are#related#through#their#LMfunctions.#

#Selected#Publications#Balasubramanyam,# B.# and# Raghuram,# A.# Special# values# of# adjoint# LMfunctions# and# congruences# for#

automorphic#forms#on#GL(n)#over#a#number#field#American*Journal*of*Mathematics#(To#appear).#

Balasubramanyam,# B.,# Ghate,# E.# and# Vatsal,# V.# (2013).#On# local# Galois# representations# over# totally# real#

fields.#Manuscripta*Mathematica#142:513M524.#Balasubramanyam,#B.#and#Longo,#M.#(2010).#∧Madic#modular#symbols#over#totally#real#fields.#Commenterii#

Mathematici*Helvetici#86:841M865.#

##

Baskar*Balasubramanyam*Assistant#Professor#[email protected]###Baskar#Balasubramanyam#completed#his#PhD#from#Brandeis#University,#USA#in#2007.#In#2007M08,#he#was#a#postdoctoral#fellow#at#the#Center#for#Advanced#Study#in#Mathematics#at#the#BenMGurion#University#of#the#Negev#in#Israel.#Following#this,#he#was#a#Bateman#Instructor#at#California#Institute#of#Technology,#USA#during#2008M10.#He#has#been#with#IISER#Pune#since#September#2010.##

#


Representation*Theory,*Analysis*&*Geometry*of*Locally*Symmetric*Spaces,*Number*

Theory*

From#last#few#years,#I#have#been#studying#the#arithmetic#aspects#of#the#spectral#theory#and#geometry#of#symmetric#spaces.#My#thesis#work#involved#proving#various#analogues#of#the#classical#number#theoretic#results#in#the#context#of#symmetric#spaces.#In#a#recent#joint# work# with#my# colleague# Dr.# Supriya# Pisolkar# from#Mathematics# group# at# IISER#Pune,# we# have# proved# some# results# on# representation# equivalence# of# discrete#subgroups#in#Lie#groups.##I#am#also#interested#in#the#study#of#analytic#properties#of#the#Zeta#functions#associated#to#a#rank#one# locally#symmetric#space.#My#students#and#me#are#working#on#some#of#the#`inverse#problems’#on#locally#symmetric#spaces#with#the#aid#of#Zeta#functions#and#harmonic#analysis.#

#Another# area# in#mathematics# that# fascinates#me# is# special# values# of# LMfunctions.#My#earlier# joint#work#with#Prof.#Raghuram#has#established#period# relations# for# the# tensor#product# of# motives.# I# am# currently# working# on# some# related# problems# about# special#values# for# automorphic#LMfunctions# associated# to# representations# of# algebraic# groups#(GL(n),# SO(n)# etc.);# using# techniques# like# Cohomology# of# arithmetic# groups# and#Langlands#constant#term#theory.#

Recently,#I#have#been#involved#in#studying#some#questions#in#spectral#graph#theory#and#their# relation#with# arithmetic,# analysis# and# geometry.# I# have#worked#with# two# of#my#colleagues# Prof.# G.# Ambika# and# Mr.# Snehal# Shekatkar# (from# Physics# group# at# IISER#Pune)#on#a#project#where#we#established# some# interesting# results# for# natural# number#network,#viewed#as#a#complex#network.#In#another#ongoing#project#with#my#colleagues#Dr.#Anisa#MHC#and#Mr.#Pralhad#Shinde#(from#Mathematics#group#at#IISER#Pune),#we#are#working#on#some#theorems#about#graph#Laplacians#which#will#be#analogues#of#certain#optimization#theorems#in#classical#geometry.#

#Selected#Publications#Shekatkar,#S.M.,#Bhagwat,#C.#and#Ambika,#G.# (2015).#Divisibility#patterns#of#natural#numbers#on#a#complex#

network.#Scientific*Reports#5,#Article#number:#14280#(2015),#doi:10.1038/srep14280#

Bhagwat,#C.#(2015).#On#Deligne#periods#for#tensor#product#motives.#Comptes*rendus*Q*Mathématique#353:191M#

195.#

Bhagwat,#C.#and#Pisolkar,#S.#(2015).#On#uniform#lattices#in#real#semisimple#group.#Proceedings*of*the*American*

Mathematical*Society#doi:#10.1090/proc/12961#

Bhagwat,#C.#and#Raghuram,#A.#Endoscopy#and#Cohomology#of#GL(N).#(Accepted#for#publication#in#the#special#

issue#of#the#BIMS#in#honor#of#Professor#Freydoon#Shahidi's#70th#birthday.)##

Chandrasheel*Bhagwat#Assistant#Professor#[email protected]###Chandrasheel#Bhagwat#completed#his#PhD#in#Mathematics#from#Tata#Institute#of#Fundamental#Research#(TIFR)#Mumbai,#India#in#2011#and#spent#a#few#months#as#a#postMdoctoral#fellow#at#IISER#Pune.#He#has#received#the#DSTMINSPIRE#faculty#award#and#research#grant#in#2011#and#has#joined#IISER#Pune#as#INSPIRE#Faculty#in#March#2012.#From#December#1,#2014,#he#has#been#working#as#an#Assistant#Professor#at#IISER#Pune.#

#


Automorphic*Forms*and*Arithmetic*Geometry*

In# arithmetic# geometry,# we# study# the# integral# solutions# of# polynomial# equations.# In#

arithmetic# geometry# we# usually# work# over# nonMalgebraically# closed# fields# (like# rational#

numbers),#and#often#in#fields#of#nonMzero#characteristic#(like#finite#fields),#and#we#may#even#

restrict#ourselves#even#to#rings#that#are#not#a#field#(like#integers).#We#use#the#rich#theory#of#

modular#forms#(more#generally,#automorphic#representations)#to#find#these#solutions.#

Modular#forms/#automorphic#forms#are#generalizations#of#the#periodic#functions#like#sine#or#

cosine.# The# theory# of# modular# forms# made# major# contributions# in# several# important#

discoveries#in#modern#mathematics,#including#the#uniform#boundedness#of#torsion#point#of#

elliptic#curves.##

I# am# interested# in# understanding# objects# in# geometry# called# “motives”# and# objects# in#

analysis# called# automorphic# representations.# The# overarching# bridge/conjecture# of#

Langlands#connects# these# two# fairly# faraway#worlds.# I# am# interested# in#understanding# the#

integral#and#pMadic#bridges#that#connect#these#two#beautiful#universes.##

In# the# automorphic# universe,# I#wish# to# focus# on#modular# symbols# and# special# values# of#LM

functions# (one# of# the# main# objects# of# study# in# the# Langlands'# program).# Motives# can# be#

described# by# different# cohomology# theories.# I# wish# to# understand# and# use# different#

cohomology#theories#using#modular#symbols,#which#in#turn#give#insights#into#special#values#

of#LMfunctions.#

In# another#work,# I# developed# the# theory# of# differential#modular# forms# for# Shimura# curves#

over# totally# real# fields.# The# differential# modular# forms# were# invented# by# Buium# and# his#

collaborators.#These#work#open#the#pMadic#bridge#of#certain#automorpic#forms.#

#Selected#Publications#Banerjee,#D.# and#Krishnamoorthy,# S.# The# Eisenstein# elements# for# level# product# of# two# odd# primes.#Pacific*

Journal*of*Mathematics#(To#appear).##

Banerjee,#D.#and#Merel,#L.#The#Eisenstein#cycles#inside#the#space#of#modular#symbols#(Preprint).#

Banerjee,#D.#and#Raghuram,#A.#pMadic#LMfunctions#for#GLn#(preprint,#expository#article)#

Banerjee,#D.# (2014).#A# note# on# the#Eisenstein# elements# of# prime# square# level.#Proceedings* of* the*American*

Mathematical*Society#142:3675M3686.#

Banerjee,#D.#(2014).#Differential#modular#forms#on#Shimura#curves#over#totally#real#fields.#Journal*of*Number*

Theory#135:353M373.#

Banerjee,# D.# and# Ghate,# E.# (2013).# Adjoint# lifts# and# modular# endomorphism# algebras.# Israel* Journal* of*

Mathematics#195(2):507M543.##

Banerjee,#D.#and#Ghate,#E.#(2011).#Crossed#product#algebras#attached#to#weight#one#forms.#Mathematical*

Research*Letters#18(1):139M149.#

#

Debargha*Banerjee*Assistant#Professor#[email protected]###Debargha#Banerjee#received#his#PhD#degree#from#Tata#Institute#of#Fundamental#Research,#Mumbai.#He#earned#his#Master’s#degree#in#Mathematics#from#Indian#Statistical#Institute#and#BSc#from#St#Xavier’s#College,#Kolkata.#He#got#the#Australian#Research#council#Discovery#postdoctoral#fellowship#for#2#years#at#the#Australian#National#University,#Canberra,#Australia.#He#was#a#visiting#scientist#at#the#IMSC,#Chennai,#India#and#later#a#guest#scientist#at#the#Max#Planck#institute#of#Mathematics,#Bonn,#Germany#before#joining#IISER#Pune#in#November#2013.##

#


Several*Complex*Variables*

My# research# interests# are# in# complex# analysis,# more# specifically# in# several# complex#variables.#Several# complex#variables# is# the#study#of#holomorphic# functions#defined#on#domains# in#Cn,#or#more#generally#on#complex#manifolds.#The#subject#established#itself#as#a#new#independent#area#of#research#in#the#early#twentieth#century#when#F.#Hartogs#discovered# a# surprising# extension# phenomenon# in# the# theory# of# functions# of# several#complex#variables#which# is#absent# in#the#theory# in#one#variable.# In#the#complex#plane,#every#domain# is#a#domain#of#holomorphy,# i.e.,# there#exists#a#holomorphic# function#on#the# domain#which# has# no# holomorphic# extension# to# a# strictly# larger# domain.#Hartogs#showed#that#this#is#no#longer#true#in#higher#dimension.#Another#astonishing#feature#of#several#complex#variables#is#the#absence#of#the#Riemann#mapping#theorem#which#was#discovered#by#Poincare#around#the#same#time#by#showing#that#the#unit#ball#and#the#unit#polydisc#in#Cn,#n#≥#2,#are#not#biholomorphic#though#both#of#them#are#simply#connected.##In#the#past,#I#studied#several#intrinsic#properties#of#a#K# ̈ahler#metric,#the#so#called#Robin#metric,#on#bounded#pseudoconvex#domains#in#Cn,#n#>#1.#This#metric#was#constructed#by#N.#Levenberg#and#H.#Yamaguchi#using# the#Robin# function# that#arises# from# the#Green#function#associated#to#the#standard#sumMofMsquares#Laplacian#in#Cn,#n#>#1.##Currently#I#am#studying#the#Green#and#Robin#functions#for#multiply#connected#domains#in#the#complex#plane.###Selected#Publications#Borah,#D.#Remarks#on#the#metric# induced#by#the#Robin# function# III.#Journal*of* the*Ramanujan*Mathematical*

Society#(Accepted#for#Publication).#

Borah,#D.# (2013).# Remarks# on# the#metric# Induced# by# the# Robin# Function# II.#Michigan*Mathematical* Journal#

62(3):581M630.#

Borah,# D.# and# Verma,# K.# (2011).# Remarks# on# the#metric# induced# by# the# Robin# function.# Indiana*University*

Mathematics*Journal#60:751M802.#

##

Diganta*Borah*Assistant#Professor#[email protected]###Diganta#Borah#received#his#PhD#from#the#Indian#Institute#of#Science#(IISc),#Bangalore,#India#in#2010#and#was#a#Research#Associate#there#until#2011.#He#joined#IISER#Pune#in#January#2012.#

#


Analytic*Number*Theory,*Harmonic*Analysis*and*Arithmetic*Geometry*

My# primary# research# work# is# concerned# with# extremal# functions# in# Fourier# analysis,#equidistribution# of# Fourier# coefficients# of# modular# cusp# forms,# EichlerMSelberg# trace#formula#and#arithmetic#of#modular#curves.#Modular#forms#play#an#extremely#important#role# in# number# theory# and# their# Fourier# coefficients# carry# fundamental# information#about# points# of# elliptic# curves# over# finite# fields,# values# of# the#partition# function,# class#numbers#and#representations#of#integers#by#quadratic#forms.#They#are#essential#tools#in#addressing#many# fundamental#problems# in#Mathematics,# like#Fermat's#Last#Theorem.#Modular# forms# are# a# special# case# of# automorphic# representations# and# lead# to# the#Langlands#program,#a# theme# that#drives#much#of# the# twenty# first# century# research# in#number# theory# and# representation# theory.# My# research# program# focuses# on# the#behavior# of# the# Fourier# coefficients# of# normalized# Hecke# eigenforms# and# their#connections#with#Jacobian#varieties#of#modular#curves.#

My# research# program# in# number# theory# heavily# draws# ideas# and# techniques# from#various# mathematical# areas,# like# harmonic# analysis# and# arithmetic# geometry.# The#problems#pursued#by#me#are#posed#in#the#language#of#algebra#and#geometry,#where#as#the# techniques# used# in# resolving# them# come# from# harmonic# analysis.# Moreover,# a#comprehensive#understanding#of#these#questions#necessitates#approaching#them#from#a#representationMtheoretic#point#of#view.#

#Selected#Publications#Bucur,#A.,#David,#C.,#Feigon,#B.,#Lalín,#M.#and#Sinha,#K.# (2012).#Distribution#of#zeta#zeroes#of#ArtinMSchreier#

covers.#Mathematical*Research*Letters.#

Lalín,#M.#and#Sinha,#K.#(2011).#Higher#Mahler#measure#for#cyclotomic#polynomials#and#Lehmer's#question.#The*

Ramanujan*Journal#26:257M294.#

Ram#Murty,#M.#and#Sinha,#K.#(2010).#Factoring#newparts#of#Jacobians#of#certain#modular#curves.#Proceedings*

of*the*American*Mathematical*Society#138:3481M3494.#

Ram#Murty,#M.#and#Sinha,#K.#(2009).#Effective#equidistribution#of#eigenvalues#of#Hecke#operators.#Journal*of*

Number*Theory#129:681M714.#

##

Kaneenika*Sinha*Assistant#Professor#[email protected]###Kaneenika#Sinha#completed#her#PhD#from#Queen's#University,#Canada#in#2006.#She#has#held#postdoctoral#fellowships#at#University#of#Toronto,#University#of#Alberta#and#Mathematical#Sciences#Research#Institute,#Berkeley.##She#was#an#assistant#professor#in#IISER#Kolkata#before#joining#IISER#Pune#in#December#2012.#

#


Algebraic*Geometric**Coding*Theory*

My# recent# work# is# about# studying# Error# Correcting# Codes# from# the# viewpoint# of#projective#geometry#over#finite#fields.#

To#give# a# flavour# of# the# kind#of# questions# I# am#working#on# currently,# consider# k# by#n#matrices#over#a#finite#field#with#q#elements#(say#q#is#odd)#such#that#all#k#by#k#minors#of#this#matrix#are#nonzero.#Let#us#call#such#a#matrix#MDS.#

Question:#What#can#we#say#about#3#by#q+1#MDS#matrices?#Segre#showed#that#any#such#matrix#is#row#equivalent#to#a#matrix#whose#columns#lie#on#the#conic#y^2#=#xz.##Question:#Do#there#exist#k#by#q+2#MDS#matrices#when#k#<q?#The#negative#answer#to#this#question#is#the#main#conjecture#about#MDS#matrices/codes.##Selected#Publications#Kaipa,#K.#(2014).#An#asymptotic#formula#in#q#for#the#number#of#[n,k]#qMary#MDS#codes.# IEEE*Transactions*on*

Information*Theory#60(11):7047M7057.#

With# Harish# Pillai# (2013).# Weight# spectrum# of# codes# associated# with# the# Grassmannian# G(3,7),# IEEE*

Transactions*on*Information*Theory#59(2):986M993.#

With# Sudhir#Ghorpade# (2013).#Automorphism#groups# of#Grassmann# codes,#Finite* fields* and* its* Applications#

23:80M102.#

With# Peter# Grinevich# (2009).# Multiscale# limit# for# finiteMgap# SineMGordon# Solutions# and# Calculation# of#

Topological# Charge# using# ThetaMfunctional# Formulae.# Proceedings* of* Steklov* Mathematical* Institute#

266(1):49M58.#

##

Krishna*Kaipa*Assistant#Professor#[email protected]###Krishna#Kaipa#obtained#a#BTech#from#IIT#Bombay#and#an##MS#degree#from#University#of#Maryland#College#Park,#both#in#Mechanical#Engineering.#He#then#pursued#a#PhD#in#Mathematics#from#University#of#Maryland,#College#Park.#He#held#assistant#professor#positions#at#IIT#Bombay#and#IISER#Bhopal#before#moving#to#IISER#Pune#in#2014.#

#


Elliptic*Partial*Differential*Equations!

My# research# interest# includes# semilinear# and# quasilinear# elliptic# partial# differential#equations# arising# from# geometry# and# physics.# I# study# existence/nonexistence# of#positive/signMchanging# solutions,# qualitative# properties# of# solutions,# regularity#properties#etc#using#the#techniques#from#nonlinear#analysis.#

One#of#my#main#research#areas#is#studying#the#second#order#and#fourth#order#semilinear#and# quasilinear# elliptic# equations# with# singularity.# Such# second# order# equations# for#example,#HardyMSobolev#type#equations#arise# in#astrophysics.#Fourth#order#equations,#for# example,# equations#with# biharmonic# operator# arise# in# continuum#mechanics,# bioMphysics,#geometry.# In#particular,# in#the#modeling#of#thin#elastic#plates,#clamped#plates#and#in#the#study#of#the#PaneitzMBranson#equation#etc.#

The# other# area# of# my# research# is# studying# the# semilinear# elliptic# equations# with#measure#data,#generalized#boundary#trace#and#generalized#boundary#value#problems.#

#Selected#Publications#Bhakta,# M.# A# note# on# semilinear# elliptic# equation# with# biharmonic# operator# and# multiple# critical#

nonlinearities.#To#appear#in#Advanced*Nonlinear*Studies.#

Bhakta,#M.#(2015).#Entire#solutions#for#a#class#of#elliptic#equations#involving#pMbiharmonic#operator#and#Rellich#

potentials.#Journal*of*Math*Analysis*and*Applications#423(2).#

Bhakta,#M#and#Marcus,#M.#(2014).#Semilinear#elliptic#equations#admitting#similarity#transformations.#Journal*

of*Functional*Analysis#267(10).#

Bhakta,#M.#and#Marcus,#M.(2014).#Reduced#limit#for#semilinear#boundary#value#problems#with#measure#data.#

Journal*of*Differential*Equations#256(8).#

Bhakta,#M,#and#Musina,#R.#(2012).#Entire#solutions#for#a#class#of#variational#problems#involving#the#biharmonic#

operators#and#Rellich#potentials.#Nonlinear*Analysis#75(9).#

Bhakta,# M.# and# Sandeep,# K.# (2012).# Poincar’eMSobolev# equations# in# the# hyperbolic# space.# Calculus* of*

Variations*and*Partial*Differential*Equations#44(1M2).#

Bhakta,#M,#and#Biswas,#A.#(2011).#HardyMSobolev#type#equations#for#pMLaplacian,#1<p<2,#in#bounded#domain.#

Differential*and*Integral*Equations#24(1M2).#

Bhakta,#M.#and#Sandeep,#K.# (2009).#HardyMSobolevMMazy’a# type#equations# in#bounded#domains,# Journal* of*

Differential*Equations#247(1).##

Mousomi*Bhakta*Assistant#Professor#[email protected]###Mousomi#Bhakta#received#her#PhD#from#TIFRMCentre#for#Applicable#Mathematics,#Bangalore,#India#in#August,#2011.#After#that#she#held#visiting#scientist#position#in#ICTP,#Trieste,#Italy#for#two#months.#Next,#she#had#postdoctoral#positions#at#Technion,#Israel#for#two#years#and#University#of#New#England,#NSW,#Australia#for#one#year#before#joining#IISER#Pune#in#August##2014.#


Dynamical*Systems*Modeling*of*Multiscale*Phenomena*in*

Biology!

Dynamical# processes# in# biology# naturally# span# several# systems# and# multiple# scales,#both# in# space# and# in# time.#We# are# interested# in# studying# the# dynamical# behavior# of#biological# processes# through# mathematical# modeling# to# complement# experimental#understanding.# My# research# focuses# primarily# on# theoretical# neuroscience,# cardiac#dynamics# and# diabetes.# Each# of# these# areas# is# rich# with# issues# that# arise# from# a#fundamental# need# to# develop# theoretical# frameworks,# and# to# handle# multiscale#dynamics#within#those.##

Our# understanding# of# glucoseMstimulated# insulin# secretion# from# the# pancreatic#endocrine# tissue,# the# islets# of# Langerhans,# has# developed# considerably# over# the# last#three# decades.# Much# of# my# recent# work# has# been# related# to# analyzing# some# newly#proposed# models# of# islet# voltage# oscillations# (called# “bursting”)# that# implicate# both#ionic# as# well# as# metabolic# activity# as# being# jointly# responsible# for# function.#Simultaneously,#we#are#also#interested#in#modeling#and#analysis#of#data#collected#from#patients# diagnosed# with# Type# 2# diabetes.# This# is# joint# work# with# researchers# at# the#University#of#Pune#and#K.#E.#M.#Hospital,#Pune.#

Although#we#are#a#dry# lab,#since#such#research# is#highly# interdisciplinary# in#nature,#we#collaborate#extensively#with#experimentalists.#

#Selected#Publications#Goel,#P.#and#Sherman,#A.# (2009).#The#geometry#of#bursting# in#the#dual#oscillator#model#of#pancreatic#betaM

cells.#SIAM*Journal*on*Applied*Dynamical*Systems*(SIADS)#8:1664M1693.##

Goel,#P.,#Sherman,#A.#and#Friedman,#A.#(2009).#Multiscale#modeling#of#electrical#and#intracellular#activity# in#

the#pancreas:#The#islet#Tridomain#equations.#SIAM*Multiscale*Modeling*and*Simulation#7:1609M1642.##

Zhang,# M.,# Fendler,# B.# Peercy,# B.,# Goel,# P.,# Bertram,# R.,# Sherman,# A.,# Satin,# L.# (2008).# Long# lasting#

synchronization# of# calcium# oscillations# by# cholinergic# stimulation# in# isolated# pancreatic# islets.#

Biophysical*Journal#95:4676M4688.##

Higgins,# E.R.,# Goel,# P.,# Puglisi,# J.L.,# Bers,# D.M.,# Cannell,# M.# and# Sneyd,# J.# (2007).# Modeling# calcium#

microdomains#using#homogenization.#Journal*of*Theoretical*Biology#247:623M644.##

Goel,# P.,# Sneyd,# J.# and#Friedman,#A.# (2006).#Homogenization#of# the# cell# cytoplasm:#The# calcium#bidomain#

equations.#SIAM*Multiscale*Modeling*and*Simulation#5:1045M1062.#

#

Pranay*Goel*Associate#Professor#[email protected]###Pranay#Goel#received#his#PhD#in#Physics#at#the#University#of#Pittsburgh,#USA.#His#postdoctoral#work#was#carried#out#at#the#Mathematical#Biosciences#Institute,#The#Ohio#State#University,#and#at#the#Laboratory#of#Biological#Modeling,#NIDDK,#National#Institutes#of#Health,#USA.#He#joined#the#Mathematics#and#Biology#faculty#at#IISER#Pune#in#2009.#

#


Classical*Algebraic*KStheory!

My#work#is#based#on#problems#in#classical#KMtheory#which#are#related#to#Serre’s#problem#on# projective# modules.# This# famous# theorem# says# that# finitely# generated# projective#modules#over#a#polynomial# ring#over#field#are#free.#This# involves#problems# in# lower#KMtheory,# in# particular# study# of# the# Whitehead# group# K1# due# to# Hyman# Bass,# which#generalizes# the#group#of#units#of#a# ring.# Initially,# these#problems#were#studied# for# the#general#linear#groups.#Then#people#started#generalizing#those#results#for#other#classical#groups#and#also#for#the#relative#cases.#At#present,#I#am#working#on#similar#problems#for#the#general#quadratic#and#the#general#Hermitian#groups#introduced#by#Anthony#Bak.#In#addition,#I#am#also#trying#to#study#few#such#problems#for#the#higher#KMgroups.##I#am#also# interested# in#commutative#algebra,#more#specifically,# in#problems#related#to#complete#intersection#theory,#which#deals#with#the#number#of#generators#of#an#ideal.#I#am#trying#to# learn#some#computational#methods#(e.g.#use#of#CoCoA#or#Macaulay2)#to#work#on#such#kind#of#problems#with#more#advanced#tools.##Recently,# I#have#developed#my# interest# in#a#very#newly#developed#subject,#viz.#Leavitt#path#algebras#(LPA),#which#is#making#a#bridge#between#algebra#and#functional#analysis.#In#the#future,#I#would#like#to#work#on#the#algebraic#and#KMtheoretic#aspects#of#LPA.##Selected#Publications#Basu,#R.#LocalMglobal#principle#for#the#general#quadratic#and#the#general#Hermitian#groups#and#the#nilpotence#

of#KH1#(Submitted).#

Basu,# R.# (2013).# On# elementary# subgroup# of# GLn# over# rings.# Ramanujan* Mathematical* Society* Newsletter#

24(3).#

Basu,#R.# (2011).#Absence#of# torsion# for#NK1(R)#over#associative# rings.# Journal*of*Algebra*and* its*Applications#

10:793M799.#

Basu,#R.#and#Rao,#R.A.#(2010).#Injective#stability#for#K1#of#regular#rings.#Journal*of*Algebra#323:367M377.#

Bak,# A.,# Basu,# R.# and# Rao,# R.A.# (2010).# LocalMglobal# principle# for# Transvection# groups.# Proceedings* of* the*

American*Mathematical*Society#138:1191M1204.#

Basu,#R.#and#Sridharan,#R.# (2007).#An#expository#article:#On#Forster's#conjecture#and# related# results.#Punjab*

University*Research*Journal.##

Rabeya*Basu*Assistant#Professor#[email protected]###Rabeya#Basu#received#her#PhD#from#Tata#Institute#of#Fundamental#Research#(TIFR),#Mumbai,#India#in#2007.#She#then#undertook#postdoctoral#work#initially#at#Harish#Chandra#Research#Institute,#Allahabad#and#later#as#an#NBHM#Fellow#at#the#Indian#Statistical#Institute,#Kolkata,#India.#She#was#in#IISER#Kolkata#as#an#assistant#professor#before#joining#IISER#Pune#in#2010.#


Low*Dimensional*Topology!

For# a# reasonably# long# period# of# time# my# research# focused# around# the# Polynomial#representation# of# long# knots.# It#was#motivated# by# the# issue# of# settling# a# long# lasting#conjecture# of# Abhayankar.# We# established# the# equivalence# between# polynomial#isotopic#classes#of#long#knots#with#the#ambient#isotopic#classes#of#classical#knots.#Thus#the# entire# knot# theory# can# be# done# over# polynomial# knot# category.# I# am# trying# to#compute# some# numerical# knot# invariants# such# as# unknotting# number# through#polynomial#knot#theory.##Quantum# topology# is# one# of# the# emerging# research# areas.# Many# knot# invariants#naturally# arise# through# nice# matrix# algebra# representation# of# interesting# quantum#groups.#They#have#been#related#to#several#models#in#statistical#mechanics.#I#would#like#to#explore#some#models#that#are#related#to#Singular#knot#theory.#I#am#also#interested#in#classical#knot#invariants#and#their#application#in#mathematics#and#biological#sciences.#My#joint#work#with#Prof#Louis#Kauffman#on#nodal*parity*invariants*of*knotted*rigid*vertex*graphs#discusses#the#application#of#this#invariant#on#protein#folding#classification.#

#Selected#Publications#Mishra,#R.# (2014).#Polynomial#unknotting#and# singularity# index.#Kyungpook*Mathematical* Journal*54(2):271M

292.#

Kauffman,#L.#and#Mishra,#R.# (2013).#Nodal#parity# invariants# for#knotted# rigid#vertex#graphs.# Journal*of*Knot*

Theory*and*its*Ramifications*22(4):1340002.#

Mishra,#R.# and#Bhushan,#S.# (2012).#Knot# theory# in#understanding#proteins.# Journal* of*Mathematical*Biology#

65:1187M1213.#

Prabhakar,#M.#and#Mishra,#R.#(2009).#Minimal#degree#sequence#for#torus#knots#of#type#(p,q).#Journal*of*Knot*

Theory*and*its*Ramifications#18:485M491.#

Prabhakar,# M.# and# Mishra,# R.# (2009).# Polynomial# representation# for# long# knots.# International* Journal* of*

Mathematical*Analysis#3:325M337.##

Mishra,#R.#(2006).#Polynomial#representations#of#strongly#invertible#knots#and#strongly#negative#amphicheiral#

knots.#Osaka*Journal*of*Mathematics#43:625M639.#

Prabhakar,#M.#and#Mishra,#R.#(2006).#Minimal#degree#sequence#of#2–bridge#knots.#Fundamenta*Mathematicae#

3:190.##

Rama*Mishra*Associate#Professor#[email protected]###Rama#Mishra#has#obtained#her#PhD#from#Indian#Institute#of#Technology#(IIT)#Bombay,#India#in#1994.#She#spent#a#few#years#with#Harish#Chandra#Research#Institute,#Allahabad#and#Indian#Statistical#Institute,#Delhi#as#a#postdoctoral#fellow#and#then#served#as#a#faculty#at#IIT#Kharagpur#and#IIT#Delhi#for#several#years.#She#worked#as#a#JSPS#fellow#at#Osaka#City#University,#Japan#for#one#year#and#as#a#visiting#faculty#at#Boise#State#University,#USA#before#joining#IISER#Pune.#


Number*Theory,*Representation*Theory*and*

Automorphic*Forms!

My#group#is#currently#studying#the#arithmetic#properties#of#special#values#of#automorphic#LM

functions.##

The# earliest# prototype#of# a# special# value#of# an# LMfunction# is# the# classical# formula#by#Euler#which#says# that# the#sum#∑# 1/n^2#of# reciprocals#of# squares#of#all#positive# integers# is#π^2/6.#

More#generally,#suppose#M#=#{a_n}#is#a#sequence#of#numbers#coming#from#some#interesting#

data,# for# example,# a_p# can#be# the#number#of# solutions#of# an# equation#modulo# a# prime#p,#

then#a#guiding#principle# in#modern#number# theory#says# that# to#study# the#sequence#M#one#

should#study#the#LMfunction#L(s,#M)#=#∑#a_n/n^s.#One#can#glean#much#information#about#the#

sequence#M#by#studying#first#the#analytic#properties,#and#second#the#arithmetic#properties#

of#L(s,M).##

The# Langlands# program,# considered# by# many# as# a# grand# unifying# principle# in# modern#

mathematics,# bridges# different# areas# of# mathematics,# like# geometry# (elliptic# curves),#

number# theory# (Galois# representations)# and# representation# theory# (automorphic# forms).#

The#central#theme#making#these#bridges#possible#is#the#notion#of#an#LMfunction.##

Our# work# uses# the# results# and# techniques# of# the# Langlands# program# to# prove# theorems#

about# special# values# of# various# LMfunctions.# These# values# encode# within# them# a# lot# of#

arithmetic#and#geometric#information#of#the#objects#to#which#the#LMfunctions#are#attached.#

In# earlier#work# stemming# from#my# thesis,#we#have#also# studied# the# representation# theory#

and#harmonic#analysis#of*pMadic#groups.#

Selected#Publications#and#Editorial#Work#Balasubramanyam,#B.,#and#Raghuram,#A.#Special#values#of#adjoint#LMfunctions#and#congruences#for#automorphic#forms#on#

GL(n)#over#a#number#field.#American*Journal*of*Mathematics#(To#appear).##

Bhagwat,#C.,#and#Raghuram,#A.#Endoscopy#and#Cohomology#of#GL(n).#To#appear#in#special#volume#of#the#Bulletin#of#Iranian#

Mathematical#Society#dedicated#to#Freydoon#Shahidi.#

Critical#values#for#RankinMSelberg#LMfunctions#for#GL(n)#x#GL(nM1)#and#the#symmetric#cube#LMfunctions#for#GL(2).#To#appear#in#

Forum*Mathematicum.##

The#Bloch#–#Kato#Conjecture#for#the#Riemann#Zeta#Function,#Editors:#John#Coates,#A.#Raghuram,#Anupam#Saikia#and#R.#

Sujatha.#pp.#312#To#be#published#by#Cambridge#University#Press.##

With#Harald#Grobner#(2014).#On#the#arithmetic#of#Shalika#models#and#the#critical#values#of#LMfunctions#for#GL(2n).#With#an#

appendix#by#Wee#Teck#Gan.#American*Journal*of*Mathematics#136:675M728.###

With#Chandrasheel#Bhagwat.#Ratios#of#periods#of#tensor#product#motives.#Mathematical*Research*Letters#20#(2013)#No.#4,#

615M628.#

With#Wee#Teck#Gan.#Arithmeticity#for#periods#of#automorphic#forms.#To#appear#in#the#Proceedings#of#the#International#

Colloquium#on#“Automorphic#representations#and#LMfunctions,”#held#in#TIFR#Mumbai,#January#2012.##

With#Günter#Harder.#Eisenstein#cohomology#and#ratios#of#critical#values#of#RankinMSelberg#LMfunctions.#C.#R.#Acad.#Sci.#Paris,#

Ser.#I#349#(2011)#719M724.###

A*Raghuram*Professor#and#Coordinator#[email protected]###After#getting#a#BTech#in#Computer#Science#and#Engineering#from#Indian#Institute#of#Technology#(IIT)#Kanpur,#Raghuram#moved#to#Mathematics#and#got#a#PhD#in#Mathematics#in#2001#from#the#Tata#Institute#of#Fundamental#Research#(TIFR),#Mumbai,#India.#He#had#postdoctoral#positions#at#University#of#Toronto,#Canada#and#TIFR,#Mumbai,#India#and#visiting#assistant#professorships#at#Purdue#University#and#University#of#Iowa,#USA.#He#joined#Oklahoma#State#University,#USA#in#2006#as#a#tenureMtrack#assistant#professor#and#was#promoted#to#associate#professor#with#tenure#in#2011.Raghuram#joined#IISER#Pune#in#December#2011#as#a#Professor#and#the#Coordinator#of#Mathematics.#His#research#has#been#partially#funded#by#the#National#Science#Foundation,#USA,#and#the#Alexander#von#Humboldt#Foundation,#Germany.#


Algebraic*Geometry!

My# research# so# far# has# dealt#with# questions# in# algebraic# geometry.#More# specifically,#with#problems#related#to#cycles#on#abelian#varieties#and#problems#related#to#moduli#of#vector#bundles#on#curves#and#surfaces.#In#cycles#I#have#been#interested#in#a#conjecture#of#Voevodsky#which#says#that#smash#equivalence#is#the#same#as#numerical#equivalence.#This#conjecture#has#some#very#nice#consequences,#for#instance,#it#implies#that#numerical#and#homological#equivalence#coincide,#which#is#suggested#by#the#standard#conjectures#of#Grothendieck.#My#work#on#moduli#of#vector#bundles#has#focused#on#proving#Torelli#theorems# and# theorems# on# rationality# of# vector# bundles.# I# am# currently# focusing# on#expanding#my#research#to#number#theory.#


Sebastian,# R.# (2013).# Smash# nilpotent# cycles# on# varieties# dominated# by# products# of# curves.# Compositio*

Mathematica#149(9):1511M1518.#

Biswas,# I.# and# Sebastian,# R.# (2013).# On# rationality# of# moduli# spaces# of# vector# bundles# on# real# Hirzebruch#

surfaces.#Proceedings*of*the*Indian*Academy*of*Sciences*Mathematical*Sciences#123(2):213M223.##

Ronnie*Sebastian*INSPIRE#Faculty#Fellow#[email protected]###After#a#Masters’#in#Mathematics#and#Scientific#Computing#from#Indian#Institute#of#Technology#(IIT)#Kanpur,#Ronnie#Sebastian#did#a#PhD#with#V#Srinivas#and#Indranil#Biswas#at#Tata#Institute#of#Fundamental#Research#(TIFR),#Mumbai.#He#then#pursued#postdoctoral#research#at#the#Institute#of#Mathematical#Sciences,#Chennai;#Humboldt#University,#Berlin#as#an#IMU#Berlin#Einstein#Foundation#Fellow;#and#at#the#Indian#Statistical#Institute,#Bangalore#before#joining#IISER#Pune#in#May#2013.#


Combinatorics*S*Covering*Arrays*and*Software*Testing!

Covering# arrays# are# combinatorial# objects# that# have# been# successfully# applied# in# the#design#of#test#suites#for#testing#systems#such#as#software,#circuits#and#networks,#where#failures#can#be#caused#by#the# interaction#between#their#parameters.#The#columns#of#a#covering# array# provide# a# test# suite# for# software# testing.# For# most# applications,# it# is#desirable# to#construct#covering#arrays#with#minimum#number#of#columns.#We#give#an#algebraic# construction# that# improves# some# of# the# best# known# covering# arrays# of#strength# four#with# three#symbols.#We#also#construct# strength# three#and#strength# four#testing#arrays#with#high#coverage.###We#perform#a#new#generalization#of#covering#arrays#called#covering#arrays#on#3Muniform#hypergraphs.##This#is#useful#in#situations#in#which#some#combinations#of#parameters#do#not#interact;#in#these#cases,#we#do#not#insist#that#these#interactions#to#be#tested,#which#allows#reductions#in#the#number#of#required#test#cases.###Finally,#we#consider#four#most#extensively#studied#graph#products#in#literature#and#give#upper# and# lower# bounds# on# the# size# of# a# covering# array# on# product# graph.# We# find#families#of#graphs#for#which#the#size#of#a#covering#array#on#product#graph#achieves#the#lower#bound.##Selected#Publications#Akhtar,# Y.,# Maity,# S.# and# Chandrashekharan,# R.C.# (2015).# Covering# arrays# of# strength# four# and# software#

testing,#In#Mathematics*and*Computing,#Springer#Proceedings#in#Mathematics#and#Statistics,#139:#391M398.##

Maity,# S.,# Akhtar,# Y.,# Chandrashekharan,# R.C.# and# Colbourn# J.C.# (2015).# Improved# strength# four# covering#

arrays#with#three#symbols#(Submitted).#

Maity,#S.,#Arackaparambil,#C.#and#Meyase,#K.#(2013).#A#new#construction#of#resilient#Boolean#functions#with#

high#nonlinearity.#Ars*Combinatoria#109:171M192.#

Maity,#S.#(2012).#3MWay#software#testing#with#budget#constraints.#IEICE*Transactions*in*Information*&*Systems#

E95MD#(9):#2227M2231.#

#

##

Soumen*Maity*Associate#Professor#[email protected]###Soumen#Maity#received#a#PhD#from#the#Theoretical#Statistics#&#Mathematics#Unit#at#Indian#Statistical#Institute,#Kolkata,#India#in#2002.##He#has#postdoctoral#experience#from#Lund#University#Sweden;#Indian#Institute#of#Management#(IIM)#Kolkata,#India;#and#University#of#Ottawa,#Canada.#Prior#to#joining#IISER#Pune#in#2009,#he#was#at#Indian#Institute#of#Technology##(IIT)##Guwahati##and##Indian##Institute##of##Technology##(IIT)#Kharagpur,#India.##


Representation*Theory**and*Canonical*Forms!

A#basic#theme# in#representation#theory#for#a#topological#group# is# the#duality#between#the#geometry#of#the#group#and#its#spectral#theory.#In#one#project,#I#study#arithmetically#interesting#representations#called#“discrete#series”#using#this#duality.#I#attempt#to#write#their#multiplicities#in#terms#of#measures#over#conjugacy#classes#of#pMadic#groups.#

In# another# project,# I# study# representations# of# isometry# groups# of# quadratic# forms,#notably# those# induced# from# a# stabilizer# P# of# a# nondegenerate# subspace.# I# show# that#relationships#between#such#representations#are#illuminated#by#first#decomposing#P#into#two#subgroups#M#and#N,#and#then#by#finding#canonical#forms#for#the#conjugation#action#of#M#on#N.#

To#introduce#another#project,#consider#square#matrices,#with#entries#modulo#a#cubefree#integer.# I# study# the# question# of# when# two# such# matrices# are# conjugate.# I# have# also#written#some#papers#regarding#when#two#germs#of#dynamical#systems#fixing#a#point#are#conjugate,#in#the#pMadic#setting.#

#Selected#Publications#Spallone,#S.# (2012).#Stable#trace#formulas#and#discrete#series#representations.#Pacific*Math*Journal#256:435M

488.##

Jenkins,#A.#and#Spallone,#S.#(2012).#Local#analytic#conjugacy#of#semiMhyperbolic#mappings#in#two#variables,#in#

the#nonMarchimedean#setting.#International*Journal*of*Mathematics#23:1250059.#

Shahidi,# F.# and# Spallone,# S.# (2010).# Residues# of# intertwining# operators# for# SO(6)# as# character# identities.#

Compositio*Mathematica#146:772M794.#

Spallone,# S.# (2008).# Residues# of# intertwining# operators# for# classical# groups.# International* Mathematics*

Research*Notices#056:37.##

Margalit,# D.# and# Spallone,# S.# (2007).# A# homological# recipe# for# pseudoMAnosovs.# Mathematical* Research*

Letters#14:853M863##

Steven*Spallone*Associate#Professor#[email protected]###Steven#Spallone#received#his#PhD#from#the#University#of#Chicago,#USA#in#2004.#Afterwards#he#did#postdoctoral#work#at#the#MaxMPlanck#Institute#in#Bonn,#at#Purdue#University,#and#at#the#University#of#Oklahoma,#USA.#He#also#visited#the#Tata#Institute#of#Fundamental#Research#(TIFR)#Mumbai,#India.#He#joined#the#faculty#of#IISER#Pune#in#July#2012.#

#


Number*Theory,*Galois*Cohomology,*Arithmetic*

Aspects*of*Symmetric*Spaces!

Broadly# speaking,#my#area#of# research# is# number# theory# and# I# have#been#working#on#problems# mostly# related# to# local# fields.# My# thesis# deals# with# questions# having# a#common#theme#of#understanding#behavior#of#norm#maps#in#Galois#extensions#of#local#fields.#As#an#application,#I#computed#the#Chow#group#of#ZeroMcycles#of#degree#zero#on#Châtelet#surfaces#over# local# fields.#This#work#relies#on#the#work#of#Bloch,#SwinnertonMDyer,#ColliotMTéllène,#Sansuc.#

In#joint#work#with#Dr#A#Hogadi,#we#proved#a#conjecture#of#Hesselholt#which#predicts#the#vanishing# of# the# cohomology# group# H1(G(L/K),W(OL))# for# a# Galois# extension# of# local#fields#L/K.#This#can#be#seen#as#an#analogue#of#Hilbert#theoremM90.#In#the#future,#I#would#like#to#work#on#generalizations#of#this#result.#

Over#the#last#couple#of#years#I#have#also#been#fascinated#by#arithmetic#aspects#of#locally#symmetric#spaces#which#are#special#type#of#manifolds.#The#theory#of#locally#symmetric#spaces#is#a#beautiful#amalgamation#of#theory#of#Lie#groups,#algebraic#groups,#analysis,#differential#geometry,#representation#theory.#In#a#joint#work#with#Prof#CS#Rajan#and#Dr#C#Bhagwat#we#have# studied# questions# related# to# commensurability# type# problems#of#these#spaces.#

Currently,# I# am# interested# in# understanding# the#work#of#Gopal#Prasad# and#Rapinchuk#which# establishes# a# connection# between# arithmetic# and# geometric# aspects# of# these#spaces,#giving#rise#to#series#of#questions#in#this#area.#

#Selected#Publications#Pisolkar,#S.#and#Rajan,#C.S.#On#the#splitting#fields#of#generic#elements#in#Zariski#dense#subgroups.#Journal*of*

Algebra#(To#appear).#

Bhagwat,# C.S.# and#Pisolkar,# S.#On# uniform# lattices# in# real# semisimple# groups.#Proceedings* of* the*American*

Mathematical*Society#(To#appear).#

Bhagwat,#C.,#Pisolkar,#S.#and#Rajan,#C.S.#(2013).#Commensurability#and#representation#equivalent#arithmetic#

lattices.#International*Mathematical*Research*Notices#doi:#10.1093/imrn/rns282##

Supriya*Pisolkar*Assistant#Professor#[email protected]###Supriya#Pisolkar#obtained#her#PhD#degree#from#Harish#Chandra#Research#Institute,#Allahabad,#India#in#2010.#She#was#a#postdoctoral#fellow#at#Tata#Institute#of#Fundamental#Research,#Mumbai#for#about#three#years#before#joining#IISER#Pune#in#December#2013.#

#


Low*Dimensional*Topology!

My#area#of#research#is#lowMdimensional#topology.#This#is#a#very#active#area#of#research#with# several# longstanding# conjectures# proved# fairly# recently,# like# Thurston’s#Geometrization# conjecture# (which# implies# the# Poincare# conjecture)# and# the# Virtual#Fibering# conjecture.# Within# lowMdimensional# topology# I# focus# mainly# on# foliations,#triangulations#and#Heegaard#splittings#of#3Mdimensional#manifolds.#

A#closed#book#looks#like#a#solid#3Mdimensional#object,#but#on#closer#analysis#is#observed#to#consist#of#2Mdimensional#pages#stacked#tightly#together.#Similarly,#every#3Mmanifold#can# be# built# by# stacking# 2Mdimensional# surfaces# tightly# together# into#what# is# called# a#foliation.# I# am# studying# a# special# class# of# foliations# called# taut# foliations#which# tell# us#useful#topological#properties#of#the#3Mmanifold.#

On#cutting#open#a#3Mmanifold#along#a#special#embedded#surface,#called#the#HeegaardMsplitting#surface,#we#end#up#with#two#simple#pieces#called#handlebodies.#Every#closed#3Mmanifold#has#such#a#splitting#surface#which#may#not#be#unique.#I#am#currently#working#on# a# structure# for# these# splitting# surfaces# when# a# 3Mmanifold# has# infinitely# many# of#them.#

Every#3Mmanifold#can#be#built#by#suitably#sticking#tetraheda#together.#Normal#surfaces#are#surfaces#embedded#particularly#`nicely'#with#respect#to#such#a#triangulation.#I#have#proved#several#results#using#normal#surfaces,#such#as#a#weak#converse#of#Haken’s#wellMknown# result# about# normality# of# incompressible# surfaces# with# respect# to# every#triangulation#of#the#3Mmanifold.#


Kalelkar,#T.# and#Roberts,#R.# (2015).#Taut# foliations# in# surface#bundles#with#multiple#boundary# components.##

Pacific*Journal*of*Mathematics#273(2):257M275.#

Gadgil,#S.#and#Kalelkar,#T.# (2013).#A#Chain#complex#and#Quadrilaterals# for#normal#surfaces.#Rocky*Mountain*

Journal*of*Mathematics,#43(2):479M487.##

Kalelkar,#T.#(2009).#Incompressibility#and#normal#minimal#surfaces.#Geometriae*Dedicata#142(1):61M70.##

Kalelkar,# T.# (2008).# Euler# characteristic# and# quadrilaterals# of# normal# surfaces.# Proceedings* of* the* Indian*

Academy*of*Sciences*Mathematical*Sciences#118(2):227M233.##

Tejas*Kalelkar*Assistant#Professor#[email protected]###After#completing#his#MSc#from#Indian#Institute#of#Technology,#Bombay,#Tejas#Kalelkar#got#his#PhD#from#Indian#Statistical#Institute,#Bangalore#in#2010.#He#was#then#a#postdoctoral#fellow#at#Institute#of#Mathematical#Sciences,#Chennai#and#a#Chauvenet#Postdoctoral#Fellow#at#the#Washington#University#in#St#Louis,#USA.#He#joined#IISER#Pune#in#December#2013.#

#


Statistics!

My# research# interests# are# in# the# areas# of# inference# in# stochastic# processes,# survival#analysis# reliability# theory# and# statistics# in# finance.# Currently# I# am# working# on# two#problems.#

#(i)# Modeling# and# analysis# of# statistical# dependence:# for# example,# in# load# sharing#systems#the#failure#of#a#component#may#reduce#(increase)#the#lifetimes#of#the#surviving#components# resulting# in# dependence# between# their# lifetimes.# (ii)# Hypothesis# testing#problems#in#competing#risks#with#missing#causes#of#failure:#the#failure#of#a#unit#is#caused#by# one# of# the# several# risks# acting# on# it.# It# is# of# interest# to# know# whether# some# risk#dominates# the# others# but# sometimes# the# actual# cause# of# failure# for# some# units# is#missing.#

#Selected#Publications#Sutar,#S.S.#and#NaikMNimbalkar,#U.V.#(2016).#A#model#for#kMoutMofMm#load#sharing#systems.#Communications*in*

Statistics*Q*Theory*and*Methods#DOI:#10.1080/03610926.2014.953691#

Sutar,#S.S.#and#NaikMNimbalkar,#U.V.# (2014).#Accelerated#failure#time#models# for# loadsharing#systems.# IEEE*

Transactions*on*Reliability#63(3):706M714.#

Deshpande,#J.V.,#Dewan,#I.#and#NaikMNimbalkar,#U.V.#(2010).#A#family#of#distributions#to#model#load#sharing#

systems.#Journal*of*Statistical*Planning*and*Inference#140(6):1441M1451.#

Lam,#K.F.,#Deshpande,#J.V.,#Lau,#E.H.,#NaikMNimbalkar,#U.V.,#Yip,#P.S.#and#Xu,#Y.#(2009).#A#test#for#constant#

fatality#rate#of#an#emerging#epidemic,#with#applications#to#the#SARS#syndrome#in#Hong#Kong#and#Beijing.#

Biometrics#64(3):869M876.##

Abegaz,# F.# and#NaikMNimbalkar,# U.V# (2008).#Modeling# statistical# dependence# of#markov# chains# via# copula#

models.#Journal*of*Statistical*Planning*and*Inference#138(4):1131M1146.##

Uttara*NaikSNimbalkar*Visiting#Faculty#[email protected]###Uttara#NaikMNimbalkar#joined#IISER#in#February#2015.#She#has#about#thirty#years#of#teaching#and#research#experience#at#the#University#of#Pune#with#visiting#positions#at#the#Michigan#State#University,#the#University#of#Edinburgh#and#University#of#Waterloo.#


Algebraic*Geometry!

My# research# can# be# divided# into# three# categories:# intersection# theory,# derived#categories,#and#TMvarieties.#

Intersection*theory*

In#intersection#theory,#one#defines#invariants#of#algebraically#defined#geometric#spaces#in#terms#of#how#the#spaces#lying#on#the#given#space#intersect#each#other.#One#can#study#those#invariants#to#determine#deep#geometric#properties#of#the#space.#

Derived*category*

Given#a#variety#(a#type#of#algebraically#define#geometric#space),#one#can#define#another#algebraic# object# called# derived# category.# It# is# known# that# a# lot# of# the# geometric#properties#of#the#space#translate#to#algebraic#properties#of#the#derived#category.#

TQvariety*

While#studying#an#object#one#many#times#first#determine#its#group#of#symmetries.#The#same#holds#for#varieties.#When#the#group#of#symmetries#contain#a#torus,#one#can,#with#some# additional# hypothesis# describe# a# variety# purely# in# terms# of# some# combinatorial#data.#Currently#I#am#working#on#such#varieties.#

#Selected#Publications#Dubey,#U.V.#and#Mallick,#V.M.#(2012).#Reconstruction#of#a#superscheme#from#its#derived#category.#Journal*of*

the*Ramanujan*Mathematical*Society#27(4).#

Dubey,#U.V.,#Mallick,#V.M.#(2012).#Spectrum#of#some#triangulated#categories.#Journal*of*Algebra#364:90M118.#

Mallick,#V.M.#(2009).#Roitman's#theorem#for#singular#projective#varieties#in#arbitrary#characteristic.#Journal*of*

KQTheory#3:501M531.##

Vivek*Mohan*Mallick*Assistant#Professor#[email protected]###After#completing#BStat#(1999)#and#MStat#(2001)#from#Indian#Statistical#Institute,#Vivek#Mallick#got#his#PhD#from#Tata#Institute#of#Fundamental#Research#(TIFR)#Mumbai,#India#in#2008.#He#has#joined#IISER#Pune#in#2012#after#completing#his#postdoctoral#research#at#the#Institute#of#Mathematical#Sciences#in#Chennai#and#Centre#de#Recerca#Matematica#in#Barcelona,#Spain.#


#Adjunct#Faculty#Members!

S*A*Katre*#Professor#&#Head#Department#of#Mathematics#University#of#Pune,#Pune#EMmail:#[email protected]############[email protected]##SA# Katre# received# Masters# degree# in# Mathematics# from# University# of# Pune# and# PhD#from# Panjab# University,# Chandigarh,# India.# He# began# his# academic# career# from# SP#College#of#Pune#and#moved#to#University#of#Pune#in#1988#as#a#faculty#member#and#has#been# there# since.# Prof# Katre’s# work# is# in# the# area# of# Algebra# and# Number# Theory,# in#particular,# cyclotomy,# number# of# points# on# curves# over# finite# fields,#Waring's# problem#for# matrices,# coding# theory,# and# group# theory.# His# pedagogical# interests# include#contributing# to# mathematics# olympiads,# open# source# mathematical# software,# and# eMlearning# in#mathematics.# Prof#Katre#had# served#as# the# editor# of# pedagological# journal#Bona* Mathematica# and# has# organized# the# NBHM# sponsored# ATM# Schools# in#Mathematics#during#2004M2012.#

####

Sujatha*Ramdorai***

Canada#Research#Chair,#Department#of#Mathematics#University#of#British#Columbia,#Canada##Sujatha#Ramdorai# obtained#her# PhD# in# TIFR/Bombay#University# in# 1992# and#was#with#TIFR#till#January#2012.#She#currently#holds#a#Canada#Research#Chair#at#the#Department#of#Mathematics,#University#of#British#Columbia.#Her#research#interests#include#Iwasawa#theory# and# the# theory# of#motives.# Prof# Ramdorai# is# a# recipient# of# the# Shanti# Swarup#Bhatnagar#Award#and#the# ICTP#Ramanujan#Award.#She#was#a#Member#of#the#National#Knowledge#Commission#and#is#a#Member#of#the#Scientific#Advisory#Council#to#the#Prime#Minister,# and# also# the# National# Innovation# Council.# She# is# also# interested# in# broader#educational#issues#and#in#policy#matters#related#to#Higher#Education#and#Research.#


Chitrabhanu*Chaudhuri*#

Chitrabhanu#did#his#PhD#in#Mathematics#from#Northwestern#University#2007M2013#and#was#a#postdoctoral#fellow#at#Max#Plank# Institute# for#Mathematics# (2013M2014)#before# joining# IISER#Pune.#His# research# revolves#around#the#topology#and#geometry#of#the#Moduli#of#Curves#over#Complex#numbers.#The#Moduli#Space#of#Curves#parameterize#algebraic#curves#or#Riemann#surfaces,#up#to#isomorphisms.#It#has#been#a#central#topic#in#mathematical#research#for#several#decades#and#brings#various#fields#of#mathematics#together,# for#example#Algebraic#Geometry,#Geometric#Group# theory#and#Teichmüller# theory.# # It#has# important# connections#with#physics#as#well.#There#are#mainly# two#directions# of# research# that# Chitrabhanu# has# pursued:# one# roughly# concerns# finding# some# bounds# on# the#topological# complexity# of# certain# partial# compactifications# on# the# Moduli# of# genus# g# curves.# This# involves#computing# certain# cohomology# groups;# and# the# other# line# of# research# is# about# certain# geometrically# relevant#subrings#of#the#cohomology#ring#of#the#Moduli#space#known#as#the#Tautological#ring.###Chaudhuri,#C.#(2015).#Equivariant#cohomology#of#certain#moduli#of#weighted#pointed#rational#curves.#Manuscripta*Mathematica##The#Cohomological#Excess#of#Certain#Moduli#Spaces#of#Curves#of#Genus#g.#International*Mathematical*Research*Notices##IMRN#(2013).#Topological#Bounds#on#Certain#open#Subvarieties#of#the#Compactified#Moduli#space#of#Curves;#PhD#thesis,#Northwestern#University#2013.#

##

Dipramit*Majumdar*#

Dipramit#Majumdar# obtained# his# PhD# from# Brandeis# University,# USA# in# 2013.# He# was# a# visiting# scientist# in# ISI#Bangalore#from#2013M2014#before# joining# IISER#Pune# in#2014.#Dipramit's# research# interest# lies# in#number#theory.#Even# though# he# is# sometimes# intrigued# by# elementary# number# theoretic# problems# such# as# Class# Groups# and#Diophantine# equations,# his# main# research# interest# lies# in# pMadic# families# of# modular# forms.# Modular# forms# are#certain#functions#on#the#complex#upper#half#planes#with#a#lot#of#symmetries.#To#a#modular#form#one#can#associate#certain#object#called#the#LMfunction.#One#of#the#most#promising#ways#to#understand#classical#modular#forms#and#their#associated#LMfunction# is#via# study#of# their#pMadic#analogue.#Study#of#pMadic#modular# forms#was# initiated#by#Serre,# later#Hida#and#then#ColemanMMazur#constructed#pMadic#familes#of# 'nice'#modular#forms,#called#Hida#family#and# eigencurve# respectively.# These# objects# plays# crucial# role# in# understanding# and# solving# many# problems# in#number# theory,# for#example,#key#step# in#MazurMWiles#proof#of# Iwasawa#main#conjecture# for# rational#numbers# is#understanding#geometry#of#the#eigencurve#at#certain#points.#Majumdar,#D.#Endoscopic#transfer#between#Eigenvarieties#for#definite#Unitary#groups.#Journal*of*Ramanujan*Matematical*Society#(To#appear)#Baskar,#B.#and#Majumdar,#D.#Ordinary#families#of#automorphic#forms#on#definite#unitary#group#Conference*Proceedings*of*pQadic*Aspects*of*

Modular*Forms#(To#appear)#Jha,#S.#and#Majumdar,#D.#Functional#equation#for#the#Selmer#group#of#nearly#ordinary#Hida#deformation#of#Hilbert#modular#forms.#Asian*Journal*

of*Mathematics#(To#appear)#Majumdar,#D.#(2015).Geometry#of#the#eigencurve#at#critical#Eisenstein#series#of#weight#2.#Journal*de*Théorie*des*Nombres*de*Bordeaux##27(1):183M

197.#Kulkarni,#M.,#Majumdar,#D.#and#Sury,#B.#(2015).#lMClass#groups#of#cyclic#extensions#of#prime#degree#l.#Journal*of*Ramanujan*Matematical*Society#

30(4):413M454.##

#####

#Postdoctoral#Fellows!


#Postdoctoral#Fellows!

Krishna*Kishore*#

Krishna# Kishore# obtained# his# PhD# from# Indiana# UniversityMBloomington,# USA,# in# December# 2014.# After# his#graduation# he# joined# IISER# Pune# from# August# 2015.# His# research# interests# include# algebraic# groups,# and#representation#theory.#In#particular,#he#works#on#the#questions#related#to#the#notion#of#representation#variety,#which#is#the#variety#of#homomorphisms#from#discrete#subgroups#of#isometries#of#hyperbolic#plane#also#referred#to#as#Fuchsian#groups.#Algebraic#invariants#associated#to#such#an#object#are#of#interest#in#the#study#of#moduli#spaces.# His# work# is# focused# on# estimating# the# dimension# of# representation# variety# of# Fuchsian# groups# in#semisimple#real#algebraic#groups#using#the#deformation#theory#of#Weil.##Krishna#Kishore,#Representation#variety#of#Fuchsian#groups#in#SO(p,q)#(submitted).#

**Shane*D’Mello*#

Shane#did#his#PhD#in#Mathematics#at#Stony#Brook#University#from#2008#to#the#end#of#2013,#under#the#guidance#of#Prof#Oleg#Viro.#Subsequently,#he#was#a#postMdoctorate#at#the#Tata#Institute#of#Fundamental#Research#until#he#joined#IISER#Pune#as#a#postMdoctorate#in#August#2015.#Shane#is#interested#in#the#topology#of#real#algebraic#varieties,#which#is#the#study#of#the#topology#of#objects#that#can#be#described#real#algebraically,#for#example#as#the# real# zero# set# of# a# real# polynomial.# Such# objects# may# arise# as# surfaces,# planar# curves,# curves# in#\mathbb{RP}^3$,#or#curves#in#some#other#real#algebraic#variety.#The#algebraic#structure#imposes#restrictions#on#the# topology# and# classifying# such# objects# for# low# degrees# has# been# the# main# motivating# problem,# but# in#attempting#to#solve#them,#many#other#interesting#questions#have#emerged#along#the#way.#Shane's#main#focus#has#been#on# curves,# especially#MMcurves,# rational# real# algebraic#plane# curves,# and# real# algebraic# knots.#He# is#currently#exploring#some#of#its#connections#with#classical#knot#theory.#He#has#also#worked#a#bit#on#enumerative#geometry.###Biswas#and#D'Mello:#A#criterion#for#MMcurves#Journal*of*the*Ramanujan*Mathematical*Society#D'Mello:#Chord#Diagrams#and#Generic#Real#Rational#Planar#Curves#of#Degree#4#International*Mathematics*Research*Notices#Biswas#and#D'Mello:#MMcurves#and#symmetric#product#(submitted)#Biswas,#D'Mello,#Mukherjee,#and#Pingali:#Rational#cuspidal#curves#on#delMPezzo#surfaces#(submitted)#D'Mello:!Classification!of!real!rational!knots!of!low!degree!in!the!38sphere!(submitted)!


#Graduate#Students,##

BS#MS#Project#Students#&#Teaching#Assistants!

Advait*Phanse*PhD#Student##Advait#has#completed#MSc#from#Sir#Parshurambhau#College#in#July#2014#and#joined#IISER#Pune#in#August#2014.#His#research#interest#lies#in#manifold#theory.#He#is#currently#working#toward#PhD#with#the#guidance#of#Dr#Tejas#Kalelkar.###Ayesha*Fatima*PhD#Student##Ayesha#completed#her#BSMMS#from#IISER#Pune#in#2012#before#joining#the#PhD#program#in#August#2013.#She#is#currently#working#toward#PhD#with#the#guidance#of#Dr#Chandrasheel#Bhagwat.#Her#interest#lies#in#Number#Theory#and#Representation#Theory.###Chaitanya*Ambi*PhD#Student##Chaitanya#completed#his#MSc#from#IIT#Kharagpur#in#2009.#He#joined#IISER#Pune#in#August#2013#as#a#Project#Fellow.#Currently,#he#is#a#PhD#student#studying#with#Prof#A#Raghuram.####Debangana*Mukherjee*PhD#Student##Debangana#completed#MSc#in#Mathematics#from#Mount#Carmel#College,#Bangalore#in#2013#and#joined#IISER#Pune#soon#after.#She#is#currently#working#with#Dr#Mousomi#Bhakta#in#the#area#of#semilinear#elliptic#partial#differential#equations.###

Girish*Kulkarni*PhD#Student##Girish#completed#MSc#Mathematics#from#IIT#Madras#in#2010#and#MSc#from#University#of#Western#Ontario,#Canada#in#2012.#Girish#joined#IISER#Pune#in#2013.#He#attended#the#Algebraic#Geoemtry#conference#at#ISI#Bangalore#in#December#2015.#He#is#working#toward#PhD#with#the#guidance#of#Dr#Amit#Hogadi.###Gunja*Sachdeva*PhD#Student##Gunja#completed#MPhil#in#Mathematics#from#Dayalbagh#Educational#Institute,#Deemed#University,#Agra#in#December#2011#and#joined#IISER#Pune#in#August#2012.#She#is#currently#working#toward#PhD#with#the#guidance#of#Prof#A#Raghuram#in#the#area#of#Number#Theory.###Hitesh*Raundal*PhD#Student##Hitesh#obtained#MSc#in#Applied#Mathematics#from#University#of#Hyderabad#and#joined#IISER#Pune#in#January#2011.#He#is#a#graduate#student#with#Dr#Rama#Mishra#in#the#area#of#knot#theory.#He#has#been#working#on#minimal#polynomial#representations#of#knots#and#trying#to#find#minimal#polynomial#degree#for#knots#up#to#six#crossings.#Also,#he#is#studying#various#types#of#spaces#of#polynomial#knots#with#some#conditions#on#degrees#of#their#component#functions.###Publications:#(1)#Mishra,#R.#and#Raundal,#H.#(2015).#Spaces#of#polynomial#knots#in#low#degree,#Journal*of*Knot*Theory*&*Its*Ramifications#24(14)#:1550073#(30#pages);#(2)#Raundal,#H.#and#Mishra,#R.#(2016)#Spaces*of*Polynomial*Knots#(Preprint).#########




Jyotirmoy*Ganguly*PhD#Student##Jyotirmoy#completed#MSc#in#Mathematics#from#University#of#Hyderabad#in#2013#and#joined#IISER#Pune#soon#after.#He#is#currently#working#with#Dr#Steven#Spallone#in#the#area#of#Representation#Theory#of#Symmetric#groups.###Makarand*Sarnobat*PhD#Student##Makarand#completed#MSc#in#Mathematics#from#Sir#Parshurambhau#College,#Pune#in#2012#and#joined#IISER#Pune#immediately#after#that.#He#is#working#with#Prof#Raghuram#toward#PhD#in#the#area#of#algebraic#number#theory#and#representations#theory.#Makarand#has#been#a#teaching#assistant#for#these#courses:#Introduction#to#Proofs;#Linear#Algebra;#Multivariable#Calculus;#and#Complex#Analysis.#He#has#attended#a#conference#on#Lie#Groups#and#Lie#Algebras#in#IIT#Bombay#in#July#2014.###Manidipa*Pal*PhD#Student##Manidipa#joined#IISER#Pune#in#January#2012.#She#has#completed#course#work,#comprehensive#exams#and#minor#thesis,#which#are#in#partial#fulfillment#of#the#PhD#program.#Her#minor#thesis#was#carried#out#with#guidance#from#Dr#Chandrasheel#Bhagwat.#Manidipa#is#presently#working#with#Dr#Baskar#Balasubramanyam#in#the#area#of#algebraic#number#theory.######

Milan*Kumar*Das*PhD#Student##Milan#completed#MSc#from#Vidyasagar#University,#West#Bengal#in#2012.#He#joined#IISER#Pune#in#August#2013.#Milan#is#working#with#Dr#Anindya#Goswami#on#stochastic#control.###Neeraj*Deshmukh*PhD#Student##Neeraj#completed#his#BSMMS#from#the#Indian#Institute#of#Science#Education#and#Research,#Mohali#in#2015#and,#subsequently,#joined#the#PhD#program#at#IISER#Pune.#He#is#currently#completing#the#coursework#requirements.###Neha*Prabhu*PhD#Student##Neha#completed#her#MSc#in#Mathematics#from#IIT#Bombay#and#joined#IISER#Pune#in#August#2012.#She#is#currently#working#toward#PhD#under#the#guidance#of#Dr#Kaneenika#Sinha.#Her#interests#lie#in#number#theory#and#representation#theory.###Prabhat*Kushwaha*PhD#Student##Prabhat#completed#MSc#from#the#Department#of#Mathematics,#Banaras#Hindu#University,#Varanasi#and#joined#IISER#Pune#in#January#2012.#He#has#successfully#completed#all#the#requirements#by#the#Institute#viz.#course#work,#comprehensive#exams#and#minorMthesis.#Prabhat#is#currently#working#with##Dr#Ayan#Mahalanobis#in#the#research#area#of#public#key#cryptography.##




Pralhad*Shinde*PhD#Student##Pralhad#completed#Masters#in#Mathematics#in#2011#from#University#of#Pune,#Pune#and#joined#IISER#Pune#in#January#2012.#He#is#working#with#Dr#Ayan#Mahalanobis#and#Dr#Anupam#Singh#in#the#areas#of#cryptography#and#computational#group#theory.###Rashmi*Kulkarni*PhD#Student##Rashmi#obtained#MSc#in#Microbiology#from#MS#University,#Baroda#and#an#MTech#from#the#Centre#for#Modeling#and#Simulation,#University#of#Pune,#Pune.#She#joined#IISER#Pune#in#August#2010#and#is#working#with#Dr#Pranay#Goel#toward#her#PhD.#Her#research#involves#quantitating#oxidative#stress#in#the#development#of#insulin#resistance.####Rohit*Joshi*PhD#Student##Rohit#has#a#Masters#degree#from#IIT#Kanpur.#He#has#completed#course#work#and#cleared#comprehensive#exams#toward#IISER#Pune’s#PhD#program#in#Mathematics#and#is#currently#working#with#Dr#Steven#Spallone.#He#was#the#winner#of#silver#medal#in#International#Mathematics#Olympiad#in#2004#while#in#his#12th#standard#and#was#chosen#as#the#IISER#Pune#Mathematics#Student#of#the#Year#in#2013.#########

Soumyadip*Thandar*PhD#Student##Soumyadip#has#completed#his#Msc#(in#Mathematics)#from#University#of#Pune#in#2015#and#joined#IISER#Pune#the#same#year.#He#is#currently#doing#his#PhD#coursework.#!#Sudhir*Pujahari*PhD#Student##Sudhir#is#working#with#Dr#Kaneenika#Sinha#and#his#research#interests#include#modular#forms,#EichlerMSelberg#trace#formula,#Maass#Forms,#Kujnetsov#trace#formula,#LMfunctions,#equidistribution#theory,#extremal#functions#in#fourier#analysis.###Publication/preprints:#1.##Meher,#J.,#Pujahari,#S.#and#Shankhadhar,#K.D.#(2015).#Sign#changes#of#coefficients#of#certain#Dirichlet#series.#Funct.#Approx.#Comment.#Math.#52(1):117M126;#2.#Pujahari,#S.#Distribution#of#gaps#of#equidistributed#sequences#(Preprint);#3.#Pujahari,#S.#Effective#joint#equidistribution#of#equidistributed#sequences#(in#preparation).#

**Suprita*Talnikar*PhD#Student##Suprita#joined#the#PhD#program#at#IISER#Pune#in#August#2015.#She#has#a#gold#medal#in#MSc#(Mathematics)#from#Visvesvaraya#National#Institute#of#Technology,#Nagpur#in#2015,#and#has#completed#BSc#from#RTM#Nagpur#University#in#2013.#She#is#interested#in#the#broad#area#of#analysis,#and#also#likes#probability#theory.#!!!!!!!!




Sushil*Bhunia*PhD#Student##Sushil#completed#MSc#(Mathematics)#in#2010#from#Jadavpur#University,#Kolkata,#India.#He#joined#IISER#Pune#in#January#2012#and#completed#coursework#along#with#comprehensive#examinations#that#are#part#of#the#graduate#program.#Sushil#is#presently#working#with#Dr#Anupam##Singh#on#algebraic#groups.#!!Tathagata*Mandal*PhD#Student##Tathagata#completed#his#MSc#in#Mathematics#from#VisvaMBharati#University,#Santiniketan,#India#in#2012.#He#joined#IISER#Pune#in#August#2013.#He#is#interested#in#Number#Theory#and#Algebraic#Geometry#and#is#presently#trying#to#understand#the#endomorphism#algebras#of#modular#motives#under#the#supervision#of#Dr#Debargha#Banerjee.##!!Yasmeen*Akhtar*PhD#Student##Yasmeen’s#primary#field#of#interest#is#combinatorics#and#graph#theory.#She#is#particularly#interested#in#the#application#of#algebraic#and#algorithmic#techniques#to#optimization#problems#related#to#different#combinatorial#structures.#Yasmeen#is#working#with#Dr#Soumen#Maity#and#the#title#of#her#thesis#is#Covering#Arrays#and#Generalizations.##Recent#Publication:##Akhtar,#Y.;#Maity,#S.#and#Chandrasekharan,#R.C:#Covering#Arrays#of#Strength#Four#and#Software#Testing,#Springer#Proceedings#in#Mathematics#and#Statistics,#Vol.#139,#2015,#391M398.##

**

Debaprasanna*Kar*Integrated#PhD#Student##Debaprasanna#has#joined#IISER#Pune#Integrated#PhD#program#in#Mathematics#in#August#2015#after#graduating#from#the#Institute#of#Mathematics#&#Applications#under#Utkal#University,#Odisha.#He#is#presently#going#through#the#coursework#of#Integrated#PhD#program#and#is#interested#in#the#research#area#of#algebra.###Neha*Malik*Integrated#PhD#Student##Neha#completed#her#BSc#(Hons)#Mathematics#from#University#of#Delhi#and#joined#IISER#Pune#as#an#Integrated#PhD#student#in#2015.#She#has#done#a#reading#project#under#the#guidance#of#Dr#Vivek#Mallick#on#Topology#for#Fall#Semester#2015.#Currently,#she#is#doing#coursework#as#a#part#of#her#program#at#IISER#Pune.###Abhinav*Sahani*BS#MS#Student##Abhinav#is#currently#working#with#Dr#Vivek#Mohan#Mallick#for#his#BS#MS#fifth#year#project#in#topics#in#commutative#algebra#and#algebraic#geometry.#**Abhishek*Kumar*Shukla*BSMMS#Student##Abhishek#is#working#with#Dr#Steven#Spallone#and#Prof#Michael#Fried#on#the#Inverse#Problem#of#Galois#Theory.#Abhishek#is#interested#in#Galois#theory#and#its#generalizations#and#in#foundations#of#mathematics.####




K*Arun*Kumar*BS#MS#Student##Arun#is#working#with#Dr#Amit#Hogadi#on#Algebraic#K#theory,#Homotopy#theory#and#their#applications#to#Algebraic#Geometry.##****Safeer*K*M*BS#MS#Student##Safeer#is#working#under#the#guidance#of#Dr#Tejas#Kalelkar#on#Riemannian#Geometry#for#his#BS#MS#final#(fifth)#year#thesis.#In#this#work#he#aims#to#understand#the#celebrated#sphere#theorem#in#differential#geometry.#His#broad#research#interests#are#in#geometry#and#topology.#**Sameer*Kulkarni*BS#MS#Student##Sameer#is#trying#to#understand#some#aspects#of#elliptic#curves#over#pMadic#fields,#specifically#a#power#series#due#to#Coleman,#which#can#be#attached#to#such#elliptic#curves.#He#is#studying#the#extra#zeros#of#pMadic#LMfunction#under#the#supervision#of#Dr#Debargha#Banerjee.###Tanmay*Patankar*BS#MS#Student#Tanmay#is#working#on#his#5thMyear#thesis,#under#the#guidance#of#Dr#Anindya#Goswami.#His#interests#include#financial#mathematics,#statistics#and#timeMseries#analysis.#His#5thMyear#project#attempts#to#address#the#problem#of#asset#pricing#in#a#semiMMarkov#modulated#market#with#timeMdependent#volatility.##

Pallavi*Kharade*Project#Fellow##Pallavi#has#completed#BSc#(Computer#Science)#from#Fergusson#college#and#MSc#(Scientific#Computing)#from#University#Of#Pune.#She#has#joined#IISER#Pune#in#February#2015#as#a#Project#Fellow#working#with#Ayan#Mahalanobis.##*Aman*Jhinga*Teaching#Assistant##Aman#has#completed#BSc#(Hons)#Maths#and#Computing#and#MSc#(Mathematics)#in#June#2012#from#Panjab#University,#Chandigarh#and#is#presently#assisting#with#teaching#at#IISER#Pune.###Sneha*Jondhale*Teaching#Assistant##Sneha#has#completed#BSc#from#PVP#College,#Pravaranagar#in#2013#and#MSc#from#University#of#Pune#in#2015.#She#is#presently#assisting#with#teaching#at#IISER#Pune.###Sucheta*Dawn*Teaching#Assistant##Sucheta#has#completed#her#BSc#in#Mathematics#from#St#Xavier's#College,#Kolkata#in#2013#and#MSc#in#Mathematics#from#University#of#Pune#in#2015.#She#has#assisted#Dr#Tejas#Kalelkar#in#conducting#the#Single#Variable#Calculus#course,#Dr#Krishna#Kaipa#in#conducting#the#Linear#Algebra#course#and#Dr#Kaneenika#Sinha#in#conducting#the#course#on#Introduction#to#Proofs.#She#is#currently#assisting#Dr#Uttara#NaikMNimbalkar#in#Probability#and#Statisics#and#Dr#Diganta#Borah#in#Multivariable#Calculus.#She#is#doing#a#reading#project#on#Algebraic#Geometry#with#Dr#Rama#Mishra.#


#Support#Staff!

R*Bhagyalaxmi*Office#Assistant##Bhagyalaxmi#completed#her#BSc#from#Osmania#University,#Hyderabad.#Microbiology,#Chemistry#and#Computer#Applications#were#the#subjects#of#her#study#in#BSc.#She#also#completed#her#MSc#in#Computer#Science#from#Annamalai#University,#Tamilnadu.#She#joined#IISER#Pune#in#December#2014#and#is#providing#administrative#support#to#the#Mathematics#group.#**Kalpesh*Pednekar*Office#Assistant##Kalpesh#Pednekar#completed#his#Bachelor#Degree#in#Commerce#from#University#of#Mumbai.#He#joined#IISER#Pune#in#March#2013#and#is#presently#assisting#Mathematics#group#in#various#administrative#responsibilities#in#addition#to#assisting#the#Physics#Group#at#IISER#Pune.#####Suvarna*Gharat*Office#Assistant##Suvarna#completed#her#BSc#in#Physics#from#Fergusson#College#and#her#postMgraduation#from#Modern#College,#Pune.#She#joined#IISER#Pune#in#July#2011#and#is#presently#assisting#the#Mathematics#group#in#various#administrative#responsibilities.#########


#Publications!

2016*#Balasubramanyam,*B.#and#Raghuram,*A.#Special#values#of#adjoint#LMfunctions#and#congruences#for#automorphic#forms#on#GL(n)#over#

a#number#field#American*Journal*of*Mathematics#(To#appear).#Bhagwat,* C.#and#Raghuram,*A.#Endoscopy#and#Cohomology#of#GL(N).# (Accepted#for#publication# in#the#special# issue#of#the#BIMS#in#

honor#of#Professor#Freydoon#Shahidi's#70th#birthday.)#Banerjee,*D.#and#Krishnamoorthy,#S.#The#Eisenstein#elements#for#level#product#of#two#odd#primes.#Pacific*Journal*of*Mathematics#(To#

appear).##Banerjee,*D.#and#Merel,#L.#The#Eisenstein#cycles#inside#the#space#of#modular#symbols#(Preprint).#Borah,* D.# Remarks# on# the#metric# induced# by# the# Robin# function# III.# Journal* of* the* Ramanujan*Mathematical* Society# (Accepted# for#

Publication).#Goswami,*A.#and#Nandan,#S.#(2016).#Convergence#of#estimated#option#price#in#a#regime#switching#market.#Indian*Journal*of*Pure*and*

Applied*Mathematics#(To#appear).#Majumdar,*D.#Endoscopic#transfer#between#Eigenvarieties#for#definite#Unitary#groups.#Journal*of*Ramanujan*Matematical*Society#(To#

appear)#Baskar,*B.#and#Majumdar,*D.#Ordinary#families#of#automorphic#forms#on#definite#unitary#group.#Conference*Proceedings*of*pQadic*

Aspects*of*Modular*Forms#(To#appear).#Sutar,#S.S.#and#NaikSNimbalkar,*U.V.#(2016).#A#model#for#kMoutMofMm#load#sharing#systems.#Communications*in*Statistics*Q*Theory*and*

Methods#DOI:#10.1080/03610926.2014.953691#Pisolkar,*S.#and#Rajan,#C.S.#On#the#splitting#fields#of#generic#elements#in#Zariski#dense#subgroups.#Journal*of*Algebra#(To#appear).#Raundal,*H.#and#Mishra,*R.#Spaces*of*Polynomial*Knots#(Preprint).#Pujahari,*S.#Distribution#of#gaps#of#equidistributed#sequences#(Preprint).###

2015*Hogadi,*A.#and#Biswas,#I.#Fundamental#group#of#quotient#singularities.#International*Mathematics*Research*Notices#(To#appear).#Anisa,*M.H.C.#and#Mahadevan,#R.#(2015).#An#eigenvalue#optimisation#problem#for#the#pMLaplacian.#Proceedings*of*the*Royal*Society*of*

Edinburgh:*Section*A*Mathematics#DOI:#10.1017/S0308210515000232#Anisa,*M.H.C.,#Mahadevan,#R.#and#Toledo,#F.#(2015).#On#the#FaberMKrahn#inequality#for#the#Dirichlet#pMLaplacian.#ESAIM:*Control,*

Optimisation*and*Calculus*of*Variations#DOI:#10.1051/cocv/2014017#Arapostathis,#A.,#Biswas,*A.#and#Pang,#G.#(2015).#Ergodic#control#of#multiMclass#M/M/N+M#queues#in#the#HalfinMWhitt#regime.#Annals*of*

Applied*Probability*25(6):3511M3570.#Atar,#R.,#Biswas,*A.#and#Kaspi,#H.#(2015).#Fluid#limits#of#G/G/#1+G#queues#under#nonMpreemptive#EarliestMDeadlineMFirst#discipline.#

Mathematics*of*Operation*Research#40(3):683M702.#Shekatkar,# S.M.,# Bhagwat,* C.# and# Ambika,# G.# (2015).# Divisibility# patterns# of# natural# numbers# on# a# complex# network.#

Scientific*Reports#5,#Article#number:#14280#(2015),#doi:10.1038/srep14280#Bhagwat,*C.#(2015).#On#Deligne#periods#for#tensor#product#motives.#Comptes*rendus*Q*Mathématique#353:191M#195.#Bhagwat,*C.#and#Pisolkar,*S.#(2015).#On#uniform#lattices#in#real#semisimple#group.#Proceedings*of*the*American*Mathematical*Society#

doi:#10.1090/proc/12961#Chaudhuri,*C.#(2015).#Equivariant#cohomology#of#certain#moduli#of#weighted#pointed#rational#curves.#Manuscripta*Mathematica##Akhtar,#Y.,#Maity,* S.#and#Chandrashekharan,#R.C.# (2015).#Covering#arrays#of#strength#four#and#software#testing,# In#Mathematics*and*

Computing,#Springer#Proceedings#in#Mathematics#and#Statistics,#139:#391M398.##Maity,* S.,#Akhtar,#Y.,#Chandrashekharan,#R.C.#and#Colbourn#J.C.# (2015).# Improved#strength# four#covering#arrays#with# three#symbols#

(Submitted).#Kalelkar,*T.#and#Roberts,#R.#(2015).#Taut#foliations#in#surface#bundles#with#multiple#boundary#components.#Pacific*Journal*of*


#Publications!

Mathematics#273(2):257M275.#Majumdar,*D.#(2015).#Geometry#of#the#eigencurve#at#critical#Eisenstein#series#of#weight#2.#Journal*de*Théorie*des*Nombres*de*Bordeaux##

27(1):183M197.#Kulkarni,#M.,#Majumdar,*D.#and#Sury,#B.#(2015).#lMClass#groups#of#cyclic#extensions#of#prime#degree#l.#Journal*of*Ramanujan*Matematical*

Society#30(4):413M454.##Jha,#S.#and#Majumdar,*D.#Functional#equation#for#the#Selmer#group#of#nearly#ordinary#Hida#deformation#of#Hilbert#modular#forms.#

Asian*Journal*of*Mathematics#(To#appear)#Mishra,*R.#and#Raundal,*H.#(2015).#Spaces#of#polynomial#knots#in#low#degree.#Journal*of*Knot*Theory*&*Its*Ramifications#24(14):1550073#

(30#pages)#Meher,#J.,#Pujahari,*S.#and#Shankhadhar,#K.D.#(2015).#Sign#changes#of#coefficients#of#certain#Dirichlet#series,#Functiones*et*

Approximatio*Commentarii*Mathematici*52(1):117M126.##!


#Colloquia#and#Seminars!

Colloquia*!1. Bhakti!Bhusan!Manna!(IISER!Pune)!

March!20,!2015,!On!a!class!of!singularly!perturbed!Elliptic!problems!for!orbit!concentrations!

2. Sudhir!Ghorpade!(IIT!Bombay)!March!27,!2015,!Counting!solutions!of!systems!of!polynomial!equations!over!finite!fields!

3. Shiva!Athreya!(ISI!Bangalore)!April!10,!2015,!Sampling!and!understanding!Statistics!of!Networks!

4. Amritanshu!Prasad!(IMSc)!!April!24,!2015,!Matrices!mod!p^k!and!k!commuting!matrices!mod!p!

5. M.!Ram!Murty!(Queen's!University,!Canada)!May!22,!2015,!The!Ramanujan!conjectures!and!aftermath!

6. Harold!Edwards!(City!University,!New!York)!!May!26,!2015,!Abel's!Theorem!

7. Kirti!Joshi!(University!of!Arizona)!!June!26,!2015,!Vector!bundles!on!Riemann!surfaces:!a!perspective!!

8. A!K!Nandakumaran!(IISc,!Bangalore)!!July!31,!2015,!On!certain!convergences:!Multi8scale,!method!of!unfolding!and!homogenization!

9. K!Srinivas!(IMSc,!Chennai)!!August!7,!2015,!Hardy's!theorem!and!its!generalization!

10. Sunil!Mukhi!(IISER!Pune)!!October!30,!2015,!Some!mathematical!results!from!Conformal!Field!Theory,!Vector8Valued!

Modular!Forms!and!Positive!q8expansions!11. Kaushal!Verma!(IISc,!Bangalore)!!

November!6,!2015,!Fatou8Bieberbach!domains!12. Sudesh!Kaur!Khanduja!(IISER!Mohali)!!

November!6,!2015,!Dedekind's!theorem!on!splitting!of!primes:!137!years!of!Journey!

13. Abhijit!Champanerka!(Department!of!Mathematics,!College!of!Staten!Island,!CUNY)!December!11,!2015,!Knot,!graphs,!geometry!and!densities!

14. Matilde!Lalin!(University!of!Montreal)!!December!18,!2015,!L8functions!of!elliptic!curves!arising!from!Mahler!measure!

15. M!Ram!Murty!(Queen's!University)!!December!26,!2015,!Twin!primes!

16. Sagun!Chanillo!(Rutgers!University)!!January!5,!2016,!The!Fundamental!Theorem!of!Calculus,!its!generalizations!to!higher!dimensions!and!Applications!to!Fluid!Mechanics!and!Magnetism!

17. Kishore!Marathe!(City!University!of!New!York,!USA)!!January!15,!2016,!Mock!Moonshine!

18. Mahendra!G!Nadkarni!(University!of!Mumbai)!February!5,!2016,!On!the!problem!of!simple!Lebesgue!Spectrum!in!ergodic!theory!

19. Manjunath!Krishnapur!(IISc,!Bangalore)!February!19,!2016!

!



Visitors’*Seminars*!1. Soumya!Bhattacharya!(CIRM,!Trente,!Italy)!

!March!31,!2015,!Factorization!of!holomorphic!eta!quotients!

2. Dheeraj!Kulkarni!(Vivekananda!University)!April!1,!2015,!Relative!symplectic!caps,!48genus!and!fibered!knots!

3. Sagar!Kolte!(TIFR!Mumbai)!!April!17,!2015,!Cuspidal!curves!on!Rational!Homology!Planes!

4. Tanmay!Deshpande!(University!of!Tokyo)!!May!1,!2015,!Algebraic!groups!over!finite!fields!and!their!representations!

5. K!V!Subrahmanyam!(CMI)!June!10,!2015,!Lower!bounds!in!Computational!Complexity!8!a!geometric!approach!

6. Siddhartha!Gadgil!(IISc)!June!12,!2015,!Enumeration!over!compact!domains!

7. Anand!Deopurkar!(Columbia!University)!!June!17,!2015,!Syzygies!of!canonical!curves!and!birational!geometry!of!M_g!

8. Kirti!Joshi!(University!of!Arizona)!!June!23,!2015,!The!dormant!operatic!locus:!recent!developments!

9. Clare!D'Cruz!(Chennai!Mathematical!Institute)!!June!26,!2015,!Set!theoretic!complete!intersections!(STCI),!Symbolic!powers!and!Groebner!basis!

10. Somnath!Jha!(JNU)!!July!1,!2015,!Functional!equation!for!Selmer!groups!

11. Varun!Thakre!(HRI)!!July!2,!2015,!HyperKahler!manifolds!and!Seiberg8Witten!equations!

12. Ambrus!Pal!(Imperial!College,!London)!!

July!6,!2015,!Crystalline!Chebotarev!density!theorems!

13. Sujit!Gujar!(École!polytechnique!fédérale!de!Lausanne!(EPFL))!July!7,!2015,!Mechanism!Design!for!heterogeneous!resource!allocation!with!strategic!agents!

14. Durgha!Prasad!Challa!(Tallinn!University!of!Technology,!Estonia)!!July!10,!2015,!The!equivalent!refraction!index!for!the!acoustic!scattering!by!many!obstacles!with!error!estimates!and!applications!

15. Sugata!Mandal!(Indiana!University,!USA)!!July!10,!2015,!Minimizing!the!first!Dirichlet!eigenvalue!of!sub8surfaces!with!amenable!fundamental!group!

16. Shashank!Kanade!(Rutgers!University)!!July!20,!2015,!Some!recent!developments!regarding!identities!of!Rogers8Ramanujan!type!

17. Nishant!Chandgotia!(University!of!British!Columbia)!August!13,!2015,!Parallelism!of!Paths!on!Graphs!

18. K!B!Athreya!(Emeritus!professor,!Iowa!State!University,!Departments!of!Mathematics!and!Statistics)!August!18,!2015,!What!is!probability!theory?!

19. Aniruddha!Pant!(AlgoAnalytics!Financial!Consultancy!Pvt!Ltd)!!August!20,!2015,!High!level!overview!of!data!science!as!applied!to!various!domains!

20. Rajesh!Kulkarni!(Michigan!State!University)!!August!21,!2015,!Ulrich!bundles!on!varieties!and!related!questions!in!Brauer!groups!

21. Joel!Reu!(Université!Paris8Sud,!Orsay,!France)!August!26,!2015,!A!relative!construction!of!motivic!Steenrod!operations!!



22. Anindya!Goswami!(IISER!Pune)!!August!27,!2015,!Statistical!Inference!in!a!Regime!Switching!Market!

23. Uttara!Naik8Nimbalkar!(IISER!Pune)!!September!11,!2015,!Kernel!functions!in!statistical!learning!and!high8dimensional!data!analysis!

24. T!V!Ramanathan!(University!of!Pune)!!September!15,!2015,!Big!&!High!Dimensional!Data!in!Finance:!Some!Statistical!Issues!

25. Arnab!Mitra!(Ben!Gurion!University)!!September!23,!2015,!Base!change!and!distinction!

26. Umesh!Dubey!(IISc,!Bangalore)!!September!28,!2015,!Singularity!category!and!Knörrer!periodicity!

27. Arnab!Mitra!(Technion!(Haifa))!!November!4,!2015,!An!introduction!to!the!structure!theory!of!p8adic!groups8Part!I!

28. November!10,!2015,!An!introduction!to!the!structure!theory!of!p8adic!groups8Part!II!

29. November!10,!2015,!How!can!we!use!combinatory!to!pick!our!ideal!partners?!

30. Vikas!Vikram!Singh!(Universite!Paris8Sud!11)!November!24,!2015,!Existence!of!Nash!equilibrium!

for!chance8constrained!games!31. Anilatmaja!Aryasomayajula!(University!of!

Hyderabad)!!December!3,!2015,!Estimates!of!Hilbert!modular!cusp!forms!of!integral!and!half8integral!weight!

32. Kishore!Marathe!(City!University!of!New!York,!USA)!December!8,!2015,!Witten's!Approach!to!38!Manifold!invariants!with!or!without!knots8Part!I!

33. December!9,!2015,!Witten's!Approach!to!38!Manifold!invariants!with!or!without!knots!part8II!

34. Guhan!Venkat!(Imperial!College,!London)!!January!5,!2016,!Darmon!cycles!and!the!kohnen8shintani!lifting!

35. Sagun!Chanillo!(Rutgers!University)!!January!6,!2016,!CR!Geometry!in!Three!Dimensions!

36. Kishore!Marathe!(City!University!of!New!York,!USA)!January!12,!2016,!Moonshine!!



Mini*Courses##

Econometrics:*Modeling*Financial*Markets*Instructor:#Vishwanathan#Iyer#(T#A#Pai#Management#Institute)#September#29MOctober#2,#2015##This#mini#course#on#Time#Series#Econometrics,#a#branch#of#computational#Finance#course#had#6#sessions#each#of# 90# minutes.# Dr# Vishwanathan# Iyer,# an# Associate# Professor# in# the# area# of# Accounting,# Economics# and#Finance# and# currently# the# Chairman# –# Admission# at# T# A# Pai#Management# Institute# (TAPMI)# conducted# all#sessions.#There#were#lab#sessions#where#participants#learned#various#useful#techniques#to#fit#linear#models#to#time#series#data.#Students#found#the#course#extremely#useful#as#they#gained#hand#on#experience#along#with#theoretical#knowledge.###

Representations*of*Reductive*pSadic*groups:*A*Short*Introduction*Instructor:#Jeff#Adler#(American#University,#Washington#DC##FebruaryMMarch,#2016##Professor#Jeff#Adler#(American#University,#Washington#DC,#USA)#gave#a#miniMcourse#of#nine#lectures#on#the#representations# of# pMadic# groups.# In# this# series# Prof# Adler# introduced# the# basic# theory# of# smooth#representations# of# reductive# pMadic# groups,# specializing# to# the# case# of# pMadic# GL2# and# culminating# in# a#classification#of#the#irreducible#representations#of#that#group.###

####



Basics*of*Shannon*Entropy*Instructor:#M#G#Nadkarni,#Professor#Emeritus,#University#of#Mumbai##Prof#Nadkarni#gave#three#lectures#in#Feb#2016#as#part#of#this#lecture#series#and#in#addition,#he#gave#a#colloquium#on#February#5,#2016#(Title:#On#the#problem#of#simple#Lebesgue#Spectrum#in#ergodic#theory).#**

Weekly*Seminar*Series*#Weekly#seminars#in#the#following#areas#have#been#held#through#the#year.#

• Algebraic*Geometry:#Homotopy#Theory#Seminar#(20#Lectures#by#Amit#Hogadi#and#Vivek#Mallick)#• Number*Theory**

• Topology**

#Homotopy*Theory*Seminar*Speakers:#Amit#Hogadi#and#Vivek#Mallick#(so#far#)*Mondays#3#to#4#pm###Lectures#1#to#6:#Speaker:#Amit#Hogadi;#Title:#Cardinals#and#Ordinals#Lectures#6#to#15:#Speaker#Vivek#Mallick;#Title:#Model#categories#and#their#homotopy#category#Lectures#15#to#20:#Speaker:#Amit#Hogadi;#Title:#Combinatorial#model#categories###Student*Seminars*The#Student#Seminar#is#a#weekly#semiMformal#event,#which#gives#a#platform#to#graduate#students,#postMdocs#and#BSMMS#students# interested# in#math#to#talk#about#their# research#or#the#math#that#they#are# learning.# It#gives#an#opportunity#to#learn#about#the#math#that#is#being#done#by#one's#peers.###The#seminars#are#hour# long#and#selfMcontained.#Some#seminars#could#be#an#overview#of#a# field#or#3M4# lectures#long,#akin#to#a#miniMcourse.###The#topics#on#which#graduate#students#spoke#included#SatoMTate#conjecture#and#Symmetric#power#L#function,#Isotopy# Extension# Theorem,# ResMInf# exact# sequence# in# group# cohomology,# Cauchy's# Definition# of# Schur#Functions,# and# Concentration# compactness# lemma.# The# BSMMS# students# talked# on# topics# like# Dirichlet's#theorem# on# primes# in# Arithmetic# progression,#Matching# Theory,# Code# Construction# for# Balanced# Arrays# and#Mathematical#Logic.##


#Symposia,#Conferences#and#Events!

The*Second*PuneSMumbai*Number*Theory*Seminar**September#25M26,#2015##Organizer:#Debargha#Banerjee##This#year’s#PuneMMumbai#Number#Theory#Seminar#had#a#new#session#exclusively#for#young#mathematicians.###

Mathematics*Symposium*September#30MOctober#1,#2015#

#Organizer:#Supriya#Pisolkar#

#Mathematics# Symposium# is# an# annual# inter# departmental#activity# where# all# members# of# the# department# attend# talks#given#by#all# faculty#and#postMdocs#on# their# research.#These#are#30# minutes# talks.# The# external# experts# Prof# C# S# Rajan# (TIFR,#Mumbai)#and#Prof#Shobha#Madan#(IIT#Kanpur)#were#present#for#this#twoMday#event.###It#was#a#very#successful#activity#where#all#students#including#PhD#students,#5th#year#and#4th#year#BS#MS#students#interacted#with#faculty# members# and# came# to# know# about# their# area# of#research.# This# is# also# an# effort# toward# having# more# internal#collaborations#within#the#department.#

Wednesday, 30th September Thursday, 1st October

Tejas Kalelkar Taut foliations in 3-manifolds

9:30 am Soumen Maity Covering arrays and generalizations

Anindya Goswami Regime switching model of financial

market

10:10 Kaneenika Sinha Equidistribution in arithmetic geometry

10:40 Tea Break

Supriya Pisolkar The inverse spectral problem

11:00 Vivek Mallick Monads in DG categories and some applications

Krishna Kaipa The MDS conjecture and the

completeness of rational normal curves over a finite field

11:40 Debargha Banerjee An explicit version of the Manin-Drinfeld theorem using Hecke operators

Shane D’Mello The topology of real algebraic curves

12:15 pm Ayan Mahalanobis An introduction to public-key cryptography

Lunch Break

Dipramit Majumdar Family of modular forms

2:30 pm Chitrabhanu Chaudhuri Equivariant cohomology of certain moduli of weighted pointed rational curves

Amit Hogadi Gabber presentation Lemma

3:10 Krishna Kishore Representation variety of Fuchsian groups in SO(p,q)

3:40 Tea Break

Anupam Kumar Singh A membership test for classical groups

4:00 Chandrasheel Bhagwat On Laplacian spectrum of graphs

Diganta Borah The Bergman metric with respect to a

certain weighted Bergman space

4:40

IISER Pune

Mathematics Symposium September 30-October 1, 2015

Indian Institute of Science Education and Research (IISER) Pune, Dr. Homi Bhabha Road, Pashan, Pune-411008, India

External Experts at the Symposium Prof. C. S. Rajan(TIFR, Mumbai) Prof. Shobha Madan (IIT, Kanpur)



Workshop*on*Hyperbolic*Knot*Theory**December#7,#2015##########

**This#workshop#was#conducted#by#Professor#Abhijit#Champanerkar#(City#University#of#New#York,#USA).#Lectures#were#on#the#basics#of#hyperbolic#geometry#in#dimensions#two#and#three.#In#addition,#techniques#in#hyperbolic#3Mmanifolds# and# hyperbolic# knots# and# links# were# taught.# Students# were# exposed# to# interactions# of# hyperbolic#geometry# to# other# areas# such# as# number# theory# (via# arithmetic# knots# and# links)# and# surface# dynamics# (via#fibered# knots# and# links).# Also#many# computational# tools# and# resources# for# various# topics# in# lowMdimensional#topology#were#introduced.#In#addition,#various#research#problems#and#research#directions#were#discussed.###

Workshop*on*Data*Analysis:*Estimation*and*Approximation*in*Science*January#6M8,#2016##Prof#L#Mahadevan,#Professor#of#Physics#and#Mathematics#from#Harvard#University#gave#a#series#of#three#lectures#on#data#analysis.#The#short#introductory#course#was#aimed#at#students/faculty#from#across#science#who#have#had#basic#mathematics#(linear#algebra,#calculus,#statistics)#and#some#computational#experience.#These#lectures#have#been#planned#to#lead#to#a#summer#workshop#by#the#same#instructor.###!



April#17,#2015:#Abel#Prize#Symposium#Talk#on#Niels#Henrik#Abel#by#Ajith#Nair,#Talk#on#Louis#Nirenberg#by#Dr#Anisa#Chorwadwala,#Talk#on#JeanMPierre#Serre#by#Prof#A#Raghuram##August#17,#2015:#Talk#on#Polynomial#formula#for#sums#of#powers#of#integers#Prof#K#B#Athreya##August#26,#2015:#Talk#on#Modelling#of#Inertial#particles#in#a#random#flow#Deeksha#Adil,#4th#year#BS#MS#student##August#28,#2015:#Talk#on#Uniform#Spaces#Visakh#Narayanan,#4th#year#BS#MS#student##August#31,#2015:#Talk#on#pMadic#numbers#Papia#Bera,#4th#year#BS#MS#student##September#2,#2015:#Talk#on#Mathematical#Logic#Varun#Prasad,#4th#year#BS#MS#student##September#4,#2015:#Talk#on#Groups,#Graphs#and#Trees#Ajith#Nair,#4th#year#BS#MS#student##September#9,#2015:#Talk#on#Code#Construction#for#Balanced#Arrays#Shreeya#Behera,#3rd#year#BS#MS#student##September#14,#2015:#Talk#on#Matching#Theory#Shipra#Kumar,#4th#year#BS#MS#student##October#9,#2015:#Talk#on#Bioinformatics#analysis#of#clonality#in#prostate#cancer#Birbal#Prasad,#5th#year#BS#MS#student##

October#12th,#14th#and#19th,#2015:#Talk#Series#on#Set#Theory#Talk#on#'Axiomatic#Theory#of#Sets'#by#Varun#Prasad,#Talk#on#'Equivalence#of#Axiom#of#choice,#Zorn's#Lemma#and#Well#ordering#theorem'#by#Visakh#Narayanan,#Talk#on#'The#centrality#of#Axiom#of#Choice#in#Mathematics'#by#Ramesh#Chandra##November#3,#2015# Talk#on#Fundamental#theorem#of#Galois#theory#for#infinite#Galois#extension#Abhishek#Shukla,#5th#year#BS#MS#student##November#6,#2015# Talk#on#Dirichlet's#theorem#on#primes#in#arithmetic#progression#Sameer#Kulkarni,#5th#year#BS#MS#student##November#10,#2015:#Talk#on#How#can#we#use#combinatorics#to#pick#our#ideal#partners?##Dr#Arnab#Mitra,#PostMDoctoral#Fellow#at#Technion,#Israel##January#27,#2015:#Introductory#Talk#of#Seminar#Series#on#Category#Theory#Varun#Prasad,#4th#year#BS#MS#student##January#29,#2015:#Talk#on#'Nonstandard#Analysis#:#Calculus#without#Epsilon#and#Delta#Prof#Jeffrey#Adler,#American#University##February#3,#2015:#Talk#on#Product,#Coproduct,#functors#etc##Visakh#Narayanan,#4th#year#BS#MS#student!

Events*Organized*by*the*Math*Club!


Mathematics*Day*2015*March*14!

Mathematics! Day! is! an! annual! student!

festival! held! to! popularize!math! among!

students!of!IISER!Pune!and!of!colleges!in!

and! around! Pune.! We! started! the! day!

with!release!of!the!Math!Profile!booklet!

that! recorded! our! yearly! departmental!

activities! followed! by! the! Math!

Clubhouse!which!was!a! series!of!games!

and! puzzles! to! encourage! students! to!

have!fun!with!math.!In!the!afternoon!we!

had! a! math! themed! skit,! quiz! and! a!

colloquium! by! an! eminent!

mathematician.!A!music!program!by!the!

students!and!a!math!movie!rounded!off!

the!day.!The!popularity!of!Math!Day!has!

been! growing! over! the! years! and! is!

steadily! chipping! away! at! the! irrational!

fear!students!have!of!this!subject.!

!


#Outreach#Activities#by#Math#Members!

Conducting#a#Math#workshop#at##Ishan#Vikas#Shibir,#May,#2016##

!


#Light#Moments!

At#the#Masquerade#Party#of#2014#Karavaan,#the#annual#cultural#fest#of#IISER#Pune#

!

The#Math#PhD#Football#Team#!

Volunteer#Meet#following##the#2014#Annual#Conference#of#the#Ramanujan#Mathematical#Society#!


#HarishMChandra’s#bust#to#be#inaugurated##

during#the#2016#Math#Day#Celebration!

Bust#of#mathematician#HarishMChandra#created#by#Charlotte#Langlands#to#be#inaugurated#during#2016#Math#day#celebration#

!

Harish# Chandra# was# born# on# 11th# October,# 1923,# in# Kanpur,# in#Uttar# Pradesh.# His# father,# Chandrakishore,# was# a# civil# engineer,#working#with# the# Indian#Service#of#Engineers#and# later# the#Uttar#Pradesh# Irrigation#Works.# His# mother# Chandrarani# came# from# a#family# of# lawyers# and# zamindars.# Harish# Chandra# grew# up# with#two#brothers#Satish#and#Suresh,#and#a#sister#Vimala.##At#the#age#of#14,# he# graduated# from# the# Christ# Church# High# School,# Kanpur.#After#intermediate#college#also#in#Kanpur,#he#obtained#his#B.Sc.#in#1941,#and#M.Sc.#in#1943#from#the#University#of#Allahabad.#For#the#M.Sc.,#he#was#examined#by#C.V.#Raman,#and#he#was#the#first#in#the#state# of# Uttar# Pradesh# to# score# full# marks# on# the# written# test.#Upon# the# advice# of# K.S.# Krishnan,# Harish# Chandra# went# to# the#Indian# Institute# of# Science# in# Bangalore# to# work# with# Homi#Bhabha.#After# two#years# at# IISc.,# he#went# to#Cambridge# to#work#with#Paul#Dirac.#He#obtained#his#Ph.D.#from#Cambridge#in#1947.#In#a# paper# communicated# by# Bhabha# to# the# Proceedings# of# the#Royal# Society,# a# copy# editor# put# a# hyphen# in# his# name,# which#Harish# Chandra# liked# very# much# and# henceforth# it# was# always#HarishMChandra.###A#paper#by#Dirac# in#1944#drew#attention#to#studying#the# infiniteMdimensional# representations# of# the# Lorentz# group,# SO(3,1)# in#

modern#notation,#with#possible#applications#to#Physics,#which#got#HarishMChandra#started#on#the#subject#that#he#was#to#revolutionize.# In# 1947M48,#HarishMChandra# accompanied#Dirac# as# his# assistant# for# a# visit# to# the# Institute#of#Advanced#Study#(IAS)#at#Princeton.#Around#this#time#he#realized#that#he#was#not#rigorous#with#his#calculations,#and#in#his#words:##“I*had* naively* manipulated* unbounded* operators* without* paying* any* attention* to* their* domains* of* definition.* I* once*

complained*to*Dirac*about*the*fact*that*my*proofs*were*not*rigorous*and*he*replied,*`I*am*not*interested*in*proofs*but*only*

in*what*nature*does.’*This* remark*confirmed*my*growing*conviction*that* I*did*not*have*the*mysterious*sixth*sense*which*

one*needs* in*order* to* succeed* in*physics*and* I* soon*decided* to*move*over* to*mathematics.”#The# rest# is#history.# #HarishMChandra#went#on#to#lay#the#foundations#of#infiniteMdimensional#representation#theory#of#Lie#groups.###From#1950#to#1963#he#was#on#the#faculty#of#Columbia#University#at#New#York#City,#and#from#1963#till#his#death#on#16th#October,#1983,#he#was#a#permanent#member#of#the#IAS#at#Princeton.#He#was#awarded#the#Cole#prize#in#Algebra#in#1954,#the#Srinivasa#Ramanujan#Medal#by#the#Indian#National#Science#Academy#in#1974,#and#the#Padma#Bhushan#in#1977.#He#was#elected#as#Fellow#of#the#Royal#Society#in#1974,#and#as#Fellow#of#the#Indian#National#Science#Academy#as#well#as#the#Indian#Academy#of#the#Sciences#in#1975.###“HarishQChandra*was*one*of*the*outstanding*mathematicians*of*his*generation,*an*algebraist*and*analyst,*and*one*of*those*

responsible* for* transforming* infiniteQdimensional* group* representation* theory* from* a* modest* topic* on* the* periphery* of*

mathematics*and*physics*into*a*major*field*central*to*contemporary*mathematics.”####M#Robert#Langlands,#Biographical#Memoirs#of#Fellows#of#the#Royal#Society#Vol#31#(1985)##

2016 IISER Pune Math Book

This is the design of a mural soon to adorn the walls of the lounge and museum room of the Math discipline at IISER Pune. The mural depicts a lounge room with John Nash, Grothendieck, Fermat, and Euler playing cards on a pi table. While Ramanujan is sleeping, Nammakal goddess is revealing to him the first Ramanujan number, as the story goes. Poincare is pouring coffee (elixir for mathematicians) out of Klein bottle into a doughnut (homotopic to mug). On the wall are Hilbert space filling curve, Fibonacci curve, tree, and Escher's painting. - Concept and Design by Devika Varma, Aswathi K T, Tanushree Shah, Shreeya Behera, Vishruta, Tejas Kalelkar


!

Indian#Institute#of#Science#Education#and#Research#(IISER)#Pune#Dr.#Homi#Bhabha#Road,#Pashan#PuneM411008,#India#Phone:#+91#20#25908001#www.iiserpune.ac.in#

Math Profile 2016 New - IISER Pune Profile 2016.pdfSneha#Jondhale# Soumen#Maity# Soumyadip#Thandar#...

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