The FMS150 conference was supported by

• The Academy of Finland

• The Finnish Cultural Foundation

• The Finnish Academy of Science and Letters

• The Finnish Society of Sciences and Letters

• The University of Helsinki

• The Finnish Centre of Excellence in Analysis and Dynamics Research

• The Finnish Centre of Excellence of Inverse Modelling and Imaging

25/10/2018, 11.51Finska Vetenskaps-Societeten – English – Finska Vetenskaps-Societeten

Page 1 of 2http://scientiarum.fi/eng/

SV (http://scientiarum.fi/) FI (http://scientiarum.fi/fi) ENG

The Finnish Society of Sciences and LettersThe Finnish Society of Sciences and Letters was founded in 1838. It is anAcademy for all branches of science and scholarship. Its aim is to promote high-qualityresearch, scholarship, networking and dissemination of information by:

arranging presentations, symposia and conferences,publishing scholarly contributions,awarding prizes,providing financial support,promoting national and international contacts,stimulating transdisciplinary discussion.

Members and sectionsMembers and sections

The Society has ordinary members, foreign members and honorary members. All membersare permanent and invited by the Plenum of the Society. At the age of 67 years, anordinary member reaches the ranks of the Seniors and a new ordinary member is invited.

The Society has four sections, each with 30 ordinary members, representing:

I mathematics and physics,II biosciences,III humanities,IV social sciences.

i

Contents

Scientific program 1Schedule and venues: . . . . . . . . . . . . . . . . . . . . . . . . . . . 1The panel discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Invited talks in alphabetical order 3Extreme values of the Riemann zeta function (Andriy Bondarenko) . . . . 3Mathematicians helping art conservators and art historians (Ingrid Daubechies

(talk cancelled)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3A New Link Between Bernoulli Percolation and the Gaussian Free Field

(Hugo Duminil-Copin) . . . . . . . . . . . . . . . . . . . . . . . . . . 4Regularity of interfaces in phase transitions via obstacle problems (Alessio

Figalli) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Dimension theory of self-similar and self-affine measures (Mike Hochman) . 4Conformal invariance in the planar Ising model: correlations and curves

(Konstantin Izyurov) . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Mathematics of 3D Genome Reconstruction in Diploid Organisms (Kaie

Kubjas) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Boundaries, conformal maps, and sub-Riemannian geometry (Enrico Le

Donne) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Recent progress in multiplicative number theory (Kaisa Matomaki) . . . . 6The (in)compatibility of 3 and 5 dimensional Heisenberg geometry with

Lebesgue spaces (Assaf Naor) . . . . . . . . . . . . . . . . . . . . . . 6Inverse problems for hyperbolic PDEs (Lauri Oksanen) . . . . . . . . . . . 7The dynamics of hard-sphere gases (Laure Saint-Raymond) . . . . . . . . . 7Inverse imaging problems and machine learning (Carola Schonlieb) . . . . 7How the lizard got its colors (Stanislav Smirnov) . . . . . . . . . . . . . . 8Loop-erased walks, SLEs, and the natural parametrization (Fredrik Viklund) 8

Practical information 9Conference venues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Lunch suggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Social program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

City of Helsinki reception . . . . . . . . . . . . . . . . . . . . . . . . 10Conference dinner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Emergency phone number in Finland: 112 . . . . . . . . . . . . . . . . . . 10

ii

Scientific program

Time Friday Time Saturday Time Sunday9.00 Coffee 9.30 Le Donne 10.00 Oksanen10.00 Opening 10.20 Coffee 10.50 Coffee10.30 Smirnov 10.50 Izyurov 11.20 Hochman11.20 Pause 11.40 Pause 12.10 Lunch11.30 Figalli 11.50 Duminil-Copin 14.00 Viklund12.20 Lunch 12.40 Lunch 14.50 Pause14.00 Panel discussion 14.30 Matomaki 15.00 Kubjas15.30 Coffee 15.20 Coffee 15.50 Coffee16.00 Saint-Raymond 15.50 Bondarenko 16.20 Naor16.50 Pause 17.10 Closing words17.00 Schonlieb17.50 Pause

16.40 Pause

19.00 Reception 19.00 Conference dinner17.30 Conference ends

Schedule and venues:

• Friday:

– The talks take place in Hall 1 (2nd floor) in the Main Building of theUniversity of Helsinki (Fabianinkatu 33).

– The panel discussion takes place in the Great Hall of the Main Building(Unioninkatu 34; the building is the same as above, but the Great Hallis most easily accessed from the Unioninkatu side).

• Saturday-Sunday: the talks on Saturday and Sunday take place in Portha-nia (Yliopistonkatu 3), hall PII in the ground floor.

• All the talks last for 50 minutes. Other activity (coffee breaks, registration)takes place in the vicinity of the corresponding scientific programme.

1

The panel discussion

The title of the panel discussion on Friday is

Mathematics in tomorrow’s society.

The panelists (in alphabetical order) are

• Prof. Jean-Pierre Bourguignon, President of the European ResearchCouncil,

• Prof. Helge Holden, NTNU Trondheim, Secretary General of the Interna-tional Mathematical Union (IMU)

• Heikki Mannila, President of the Academy of Finland

• Jorma Ollila, CEO of Nokia 1992-2006, Chairman of Royal Dutch Shell 2006-2015,

• Prof. Stanislav Smirnov, Chebyshev Laboratory, St. Petersburg StateUniversity, and University of Geneva.

The panel is chaired by Prof. Antti Kupiainen, University of Helsinki.

2

Invited talks in alphabetical order

Extreme values of the Riemann zeta function Sat 15:50

Andriy Bondarenko

NTNU, Trondheim

We prove that for every c < 1 there exists arbitrarily large T with

|ζ(1/2 + iT )| > exp(c√

log T log log log T/ log log T).

This improves classical results by Montgomery, Balasubramanian-Ramachandra,and Soundararajan. We will discuss the main components of the proof: Soundarara-jan’s resonance method, multiplicative functions, and convolution formulas for theRiemann zeta function. Further applications of the suggested approach will be con-sidered.

Mathematicians helping art conservators and art historians

Ingrid Daubechies (talk cancelled)

Duke University

Mathematics can help Art Historians and Art Conservators in studying and under-standing art works, their manufacture process and their state of conservation. Thepresentation will review several instances of such collaborations in the last decade orso. Some of them led (and are still leading) to interesting new challenges in signaland image analysis. In other applications we can virtually rejuvenate art works,bringing a different understanding and experience of the art to museum visitors aswell as to experts

3

A New Link Between Bernoulli Percolation and theGaussian Free Field Sat 11:50

Hugo Duminil-Copin

IHES

Percolation models describe the inside of a porous material. The theory emergedtimidly in the middle of the twentieth century before becoming one of the majorobjects of interest in probability and mathematical physics. In this talk, we provethat Bernoulli percolation on graphs with isoperimetric dimension d > 4 undergoesa non-trivial phase transition by exhibiting a new link between Bernoulli percolationand the Gaussian Free Field (GFF). As a corollary, we obtain that the critical pointof Bernoulli percolation on infinite Cayley graphs with super-linear growth is strictlysmaller than one, thus answering a conjecture of Benjamini and Schramm.

Regularity of interfaces in phase transitions via obstacleproblems Fri 11:30

Alessio Figalli

ETH, Zurich

The so-called Stefan problem describes the temperature distribution in a homoge-neous medium undergoing a phase change, for example ice melting to water. Animportant goal is to describe the structure of the interface separating the two phases.In its stationary version, the Stefan problem can be reduced to the classical obstacleproblem, which consists in finding the equilibrium position of an elastic membranewhose boundary is held fixed and which is constrained to lie above a given obstacle.The aim of this talk is to give a general overview of the classical theory of the ob-stacle problem, and then discuss recent developments on the structure of interfaces,both in the static and the parabolic settings.

Dimension theory of self-similar and self-affine measures Sun 11:20

Mike Hochman

The Hebrew University, Jerusalem

Dimension theory of self-similar and self-affine measures Abstract: I will sketchrecent progress on the dimension theory of self-similar and self-affine measures andtry to explain some of the ideas that have been driving them.

4

Conformal invariance in the planar Ising model:correlations and curves Sat 10:50

Konstantin Izyurov

University of Helsinki

We will review our joint results with D. Chelkak and C. Hongler on conformalinvariance of the scaling limit of the critical planar Ising model, both on the levelof correlations of local fields and of random curves interfaces. We will also reporton the ongoing progress in relating these two pictures, as well as extending theseresults to more general families of graphs and beyond the planar case.

Mathematics of 3D Genome Reconstruction in DiploidOrganisms Sun 15:00

Kaie Kubjas

Aalto University

The 3D organization of the genome plays an important role for gene regulation.Chromosome conformation capture techniques allow one to measure the number ofcontacts between genomic loci that are nearby in the 3D space. In this talk, westudy the problem of reconstructing the 3D organization of the genome from wholegenome contact frequencies in diploid organisms, i.e. organisms that contain twoindistinguishable copies of each genomic locus. This talk is based on joint work withMohab Safey El Din, Lawrence Sun and Caroline Uhler.

Boundaries, conformal maps, and sub-Riemannian geometry Sat 9:30

Enrico Le Donne

University of Jyvaskyla

The objective of this talk is to give a new point of view for the validity of Fefferman’smapping theorem from 1974. This result states that a biholomorphism between twosmoothly bounded strictly pseudoconvex domains in Cn extends as a smooth dif-feomorphism between their closures. Following ideas from Gromov, Mostow, andPansu, we discuss a method of proof in the context of quasi-conformal geometry. Inparticular, we show that every isometry between smoothly bounded strictly pseudo-convex domains is 1-quasi-conformal with respect to the sub-Riemannian distancedefined by the Levi form on the boundaries. Subsequently, a PDE argument showsthat such maps are smooth. This method was proposed by M. Cowling, and it hasbeen implemented in collaboration with L. Capogna, G. Citti, and A. Ottazzi.

5

Recent progress in multiplicative number theory Sat 14:30

Kaisa Matomaki

University of Turku

Multiplicative number theory aims to understand the ways in which integers fac-torize, and the distribution of integers with special multiplicative properties (suchas primes). It is a central area of analytic number theory with various connectionsto L-functions, harmonic analysis, combinatorics, probability etc. At the core ofthe subject lie difficult questions such as the Riemann Hypothesis, and they set abenchmark for its accomplishments.

An outstanding challenge in this field is to understand the multiplicative prop-erties of integers linked by additive conditions, for instance n and n + 1. A centralconjecture making this precise is the Chowla-Elliott conjecture on correlations ofmultiplicative functions evaluated at consecutive integers. Until recently this con-jecture appeared completely out of reach and was thought to be at least as difficultas showing the existence of infinitely many twin primes. These are also the kind ofquestions that lie beyond the capability of the Riemann Hypothesis.

However recently the landscape of multiplicative number theory has been chang-ing and we are no longer so certain about the limitations of our (new) tools. I willdiscuss the recent progress on these questions.

The (in)compatibility of 3 and 5 dimensional Heisenberggeometry with Lebesgue spaces Sun 16:20

Assaf Naor

Princeton University

The 3-dimensional (discrete) Heisenberg geometry is the shortest-path metric onthe infinite graph whose vertex set is the integer grid Z3 and the neighbors of eachinteger vector (a, b, c) are the four integer vectors

(a+ 1, b, c), (a− 1, b, c), (a, b+ 1, c+ a), (a, b− 1, c− a).

Analogously, the 5-dimensional (discrete) Heisenberg geometry is the shortest-pathmetric on the infinite graph whose vertex set is the integer grid Z5 and the neighborsof each integer vector (a, b, c, d, e) are the eight integer vectors (a±1, b, c, d, e), (a, b±1, c, d, e), (a, b, c ± 1, d, e ± a), (a, b, c, d ± 1, e ± b). The purpose of this talk is todescribe the culmination of a multi-decade effort to understand the extent to whichthese metric spaces can be represented faithfully as subsets of an Lp(µ) space. Itturns out that if p > 1, then there is no qualitative difference between the answerto this question in dimensions 3 and 5. However, if p = 1, then the behaviors ofdimensions 3 and 5 diverge markedly. These results rely on several ideas and toolsthat were introduced over the years, and they relate deeply to a rich variety ofmathematical disciplines. They answer major open questions in metric embeddings,Lipschitz factorization, dimension reduction, and semidefinite programming. Wewill describe key statements and ideas while highlighting the most recent step which

6

introduces the notion of a foliated corona decomposition (joint work with RobertYoung).

Despite the fact that our discussion is linked to a wide range of areas of mathe-matics, the talk is intended for a general audience of mathematicians and theoreticalcomputer scientists. We will not rely on any prerequisites beyond an undergraduatedegree in mathematics, and all of the relevant background will be introduced andexplained.

Inverse problems for hyperbolic PDEs Sun 10:00

Lauri Oksanen

University College of London

We discuss some recent results concerning coefficient determination problems forhyperbolic partial differential equations, both linear and non-linear. Such problemsarise for example in the context of geophysical imaging. Special attention will bepayed to the geometric features of the solution methods and the associated geo-metric assumptions. In the linear case the known results are essentially confinedto geometries of cylinder type, whereas some non-linear cases allow for much moregeneral geometries.

The dynamics of hard-sphere gases Fri 16:00

Laure Saint-Raymond

Ecole normale superieure, Lyon

We will review in this talk some important results describing the statistics of largesystems of small spheres out of equilibrium. In the Boltzmann-Grad scaling, almostsurely, the dynamics is a combination of transport and collisions, described by theBoltzmann equation. Dissipation corresponds to the delation of some informationencoded in singular subsets of the phase space. Fluctuations around this averagedynamics look like white noise.

Inverse imaging problems and machine learning Fri 17:00

Carola Schonlieb

Univerisity of Cambridge

In this talk we will showcase some recent machine learning approaches to the solu-tion of inverse imaging problems. The journey will take us from bilevel learning fortotal variation type regularisation models to task-oriented learned iterative recon-struction with neural networks and adversarial regularisers. The talk is furnishedwith applications to image de-noising, computed tomography and MRI.

7

How the lizard got its colors Fri 10:30

Stanislav Smirnov

University of Geneva

It has been proposed by Turing that in many animals, skin color patterns emergefrom nonlinear dynamical microscopic systems of cell interactions, governed by thereaction-diffusion equations. Over the last two decades it was shown to be thecase for a number of species. However, there are some puzzling examples, suchas the occelated lizard: it has a quasi-hexagonal lattice of skin scales, and those,rather than individual chromatophore cells, establish a green and black labyrinthinepatterns. Moreover, the scales occasionally flip colors, resembling a von Neumanncellular automaton. We will report on our collaboration with biologists from thelaboratory of Michel Milinkovitch, where we were able to explain how a continuousTuring reaction-diffusion system can lead to a discrete one on the lattice of scales,which in turn produces a cellular automaton. Moreover, the latter has an intriguingconnection to the Ising model.

Loop-erased walks, SLEs, and the natural parametrization Sun 14:00

Fredrik Viklund

KTH, Stockholm

SLE curves are universal scaling limits of interfaces in planar critical lattice models.These random fractal curves are constructed using Loewner?s differential equationfrom which they inherit the so-called capacity parametrization. For many problemsit is, however, better to parametrize differently and use what is often called theNatural Parametrization. I will survey some of the recent progress on understandingSLE in this parametrization and then discuss a few related results for lattice models,focussing in particular on loop-erased random walk, the self-avoiding walk one getsby erasing loops from a simple random walk. This talk is in part based on jointworks with Christian Benes and Greg Lawler.

8

Practical information

Conference venues

Below is a map of some of the main locations of the conference, and their relationto other landmarks.

07/11/2018, 10.41Porthania – Google Maps

Page 1 of 3https://www.google.com/maps/place/Porthania/@60.1708535,24.94…0bce7b4d6c8d:0x193b4ad0ac11bf04!8m2!3d60.1701225!4d24.9485189

Karttatiedot ©2018 Google 50 m

Porthania4,0 · 10 arvostelua

Yliopiston laitos

Yliopistonkatu 3, 00100 Helsinki

5WCX+2C Helsinki

helsinki.F

029 41911

Porthania

Railwaystation

Ateneum

Porthania

Mainbuilding

SokosHotel

Lunch suggestions

Here are a few restaurants in the vicinity of the conference venues. Most of themserve lunch on Friday, and a la carte over the weekend.

Conference

Base CampMomo Toko

Hanko Sushi Unicafe

Engel, Sunn,Köket

Via Tribunali

Vaelsa

Market Square

9

• Nepalese restaurant Base Camp, about 100m down the street from Porthania.Daily lunch, tasty and large curries with naan. There’s also a ramen noodleplace, Momo Toko, next door.

• Several restaurants directly opposite the big white church (e.g. Cafe Engel,Restaurant Sunn).

• Pizzeria Via Tribunali (on a narrow street, Sofiankatu, starting opposite thebig white church) and Italian restaurant Vaelsa (only opens at 2pm on Sunday).

• Restaurants inside the building opposite Porthania: e.g. Belge or Hanko Sushi(latter closed on Sunday). The coffee shop Fratello also serves lunch on Friday.

• Ateneum Bistro (big art museum on the railway square, visible on the confer-ence venues map). Daily lunch.

• Ryan Thai, a Thai restaurant on Vuorikatu 18 (not on map above) about 10minutes’ walk from Porthania.

• Friday only: Unicafe Porthania (in the conference building, one flight ofstairs up). There’s another Unicafe in the main building of the university(diagonally opposite Porthania).

Social program

City of Helsinki reception

On Friday evening, starting at 19.00, there will be a reception at Aleksanterinkatu20 (Vanha Raatihuone, Empiresali), hosted by the city of Helsinki. Aleksanterinkatu20 is located a few hundred metres east from the conference venue.

Conference dinner

The conference dinner takes place on Saturday evening, starting at 19.00, in restau-rant Sipuli (Kanavaranta 7). The walking distance from the conference venue isabout 700m.

Emergency phone number in Finland: 112

10