January 2010 - Talks › files › math › imce › 2010.pdf · domains) are the moduli spaces for...

January 2010 - Talks Contact Marie Taris for details.

Tuesday, January 19 Colloquium Time: Tea: 4:00-4:30pm Talk: 4:30-5:30pm Location: Cupples I, Room 199 Hosts: Prof. Richard

Rochberg

Speaker: Professor Jason DeBlois Department of Mathematics, University of Illinois at Chicago Title: Rank and rank gradient of groups that split Abstract: The rank of a finitely generated group G -- the minimal cardinality of a generating set -- provides a coarse measure of the complexity of G. In particular, results like Grushko's theorem relate the rank of groups that "split" to the objects involved in their decompositions. I will discuss applications of such theorems to questions about rank gradient, which measures the growth of rank in families of finite-index subgroups, and relate them to the "rank vs Heegaard genus" question for 3-manifolds. Then I will describe how geometric methods can be used to improve

estimates in some circumstances, and show why this matters for rank gradient. Thursday, January 21 Colloquium

Time: Tea: 4:00-4:30pm Talk: 4:30-5:30pm Location: Cupples I, Room 199 Hosts: Prof. Mohan Kumar

Speaker: Professor Karl Schwede Department of Mathematics, University of Michigan Title: Singularities of polynomials in characteristic 0 and characteristic p Abstract: I will discuss the singularities of the zero-locus of a complex valued polynomial equation. A particular focus will be payed to comparing different singularities. I will discuss two different approaches to this question, both analytic (characteristic zero) and algebraic (positive characteristic).

Monday, 25 Colloquium Time: Tea: 4:00-4:30pm Talk: 4:30-5:30pm Location: Cupples I, Room 199 Hosts: Prof. Mohan Kumar

Speaker: Professor Matthew Kerr Department of Mathematics, Durham University, United Kindom Title: Mumford-Tate groups and the classification of Hodge structures Abstract: Since their introduction in the mid-20th Century, Hodge structures have been a fundamental tool in transcendental algebraic geometry, for example in the study of algebraic cycles and moduli of complex algebraic varieties. Mumford-Tate groups are the symmetry groups of Hodge theory, and their orbits (Mumford-Tate domains) are the moduli spaces for Hodge structures with given symmetries. The 'classical' case of Hodge structures of weight 1 (and those they generate by linear-algebraic constructions) has been thoroughly studied. In this case, the MT-domains are Hermitian symmetric spaces whose arithmetic quotients yield algebraic (Shimura) varieties. The many beautiful results facilitated by MT groups in this setting include Deligne's theorem on absolute Hodge cycles and the resolution (by many authors) of the full Hodge conjecture for various classes of abelian varieties. Following on a review of this history, I will describe recent joint work with P. Griffiths and M. Green on the "nonclassical" higher weight case. The corresponding theory is in its early stages and is of an entirely different character: Shimura varieties are replaced by global integral manifolds of an exterior differential system, and nonclassical (exceptional) Lie groups turn out to occur as MT groups. In addition to the general context mentioned above, part of the motivation for our project was to better understand the very interesting special features of period domains associated to Calabi-Yau 3-folds, and I will explain a classification result for the MT subdomains in an important special case.

Tuesday, January 26 Algebraic Geometry Seminar Time: 4:00-5:30pm Location: Cupples I, Room 216 Hosts: Prof. Mohan Kumar

Speaker: Professor Matthew Kerr Department of Mathematics, Durham University, United Kindom Title: A Tour of Normal Functions and Algebraic Cycles Abstract: Associated to a pencil of algebraic curves with singular fibres is a bundle of Jacobians (which are abelian varieties off the discriminant locus of the family and semiabelian varieties over it). Normal functions, which are holomorphic sections of such a Jacobian bundle, were introduced by Poincare and used by Lefschetz to prove the Hodge Conjecture (HC) on algebraic surfaces. By a recent result of Griffiths and Green, an appropriate generalization of these normal functions remains at the center of efforts to establish the HC more generally and understand its implications. (Furthermore, the nature of the zero-loci of these normal functions is related to the Bloch-Beilinson conjectures on filtrations on Chow groups.)

Abel-Jacobi maps give the connection between algebraic cycles and normal functions. In this talk, we shall discuss the limits and singularities of Abel-Jacobi maps for cycles on degenerating families of algebraic varieties. These two features are strongly connected with the issue of graphing admissible normal functions in a Neron model, properly generalizing Poincare's notion of normal functions. Some of these issues will be passed over rather lightly; our main intention is to give some simple examples of limits of AJ maps and stress their connection with higher algebraic K-theory. A very new theme in homological mirror symmetry concerns what the mirror of a normal function should be; in work of Morrison and Walcher, the mirror is related to counting holomorphic disks in a CY 3-fold bounding on a Lagrangian. Along slightly different lines, we shall briefly describe a surprising application of "higher" normal functions to growth of enumerative (Gromov-Witten) invariants in the context of local mirror symmetry.

Wednesday, January 27 Colloquium Time: Tea: 4:00-4:30pm Talk: 4:30-5:30pm Location: Cupples I, Room 199 Hosts: Prof. Xiang Tang

Speaker: Professor Guoliang Yu Department of Mathematics, Vanderbilt University Title: Group actions and their applications to K-theory Abstract: I will discuss how to realize groups as symmetries of nice geometric objects and apply such constructions to compute K-groups. The computation of K-groups has interesting applications to problems in algebra such as the idempotent conjecture. This talk should be accessible to non-experts.

February 2010 - Talks Contact Marie Taris for details.

Monday, February 01 Colloquium Time: Tea: 4:00-4:30pm Talk: 4:30-5:30pm Location: Cupples I, Room 199

Host: Prof. Richard Rochberg

Speaker: Professor Vasiliy Dolgushev Department of Mathematics, University of California, Riverside Title: Puzzles of Deformation Theory Abstract: A lot of interesting mathematical constructions are motivated by questions of deformation quantization. In my talk I will give a popular introduction to this fascinating topic. First, I will show that formal deformations of an associative algebra are governed by the Hochschild cochain complex. Second, I will discuss algebraic operations on this complex. Then I will formulate the famous Kontsevich's formality theorem and talk about its generalizations. Finally, I will discuss applications of formality theorems for Hochschild complexes to computation of Hochschild (co)homology and description of traces on deformation quantization algebras. If time will permit then I will also talk about the Kashiwara-Vergne conjecture and about the mysterious action of the Grothendieck-Teichmuller group

on deformations of the polynomial algebra. Wednesday, February 03 Graduate Student Seminar

Time: 1:00-2:00pm Location: Cupples I, Room 199

Host: Prof. Guido Weiss

Speaker: Professor Xiang Tang Department of Mathematics, Washington University in St. Louis Title: Laplace operator and Hodge decomposition Abstract: In this talk, we will introduce the Beltrami-Laplace operator on a compact riemannian manifold. We will explain how to use this operator to study geometry and topology of the riemannian manifold. If time permits, we will discuss a generalization of the Beltrami-Laplace operator on a noncompact riemannian manifold with a

proper cocompact group action. Wednesday, 03 Graduate Organized Talks Seminar


Host: Raphiel Murden

Speaker: Qingyun Wang Department of Mathematics, Washington University in St. Louis Title: Introduction to sheaf cohomology Abstract: Cohomology, being the dual of homology, is one of the fundamental ideas

in algebraic topology. We have various cohomology theories for different spaces. For topological spaces, we have singular cohomology. For cell complexes or CW-complexes we have cellular cohomology and CW-cohomology. For manifold we have de Rham cohomology... Even though these cohomology theories appear to be very different from the definitions, they share many common properties. Sheaf cohomology is a way to unify all these cohomology theories in a natural way and gives

an axiomatic characterization. De Rham theorem is therefore a direct consequence. Wednesday, February 03 Math Club


Host: Rajan Mehta

Movie: A Beautiful Mind

Thursday, February 04 Combinatorics Seminar


Host: Russ Woodroofe

Speaker: Russ Woodroofe Department of Mathematics, Washington University in St. Louis Title: Chordal clutters and k-decomposability Abstract: The family of chordal graphs has excellent properties for geometric combinatorics. Most interesting to us in this talk is that the independence complex of a chordal graph is shellable, and in fact vertex decomposable. I'll present an extension of the definition of chordal from graphs to clutters. The resulting family of clutters is a common generalization of chordal graphs, circuit clutters of matroids, and "acyclic" clutters. The independence complex of a chordal clutters is shellable. In order to prove shellability we extend the definition of k-decomposable to non-pure complexes. I will also discuss a potential application in obstructions to shellability, as

well as other nice properties of chordal graphs that are satisfied by chordal clutters. Thursday, February 04 Colloquium

CANCELLED Time: Tea: 4:00-4:30pm Talk: 4:30-5:30pm Location: Cupples I, Room 199

Host: Prof. Richard Rochberg

CANCELLED Speaker: Professor Richard Kent Department of Mathematics, Brown University Title: Analytic functions from hyperbolic manifolds Abstract: At the heart of Thurston's proof of Geometrization for Haken manifolds is a family of analytic functions between Teichmuller spaces called "skinning maps." These maps carry geometric information about their associated hyperbolic manifolds, and I'll discuss what is presently known about their behavior. The ideas

involved form a mix of geometry, algebra, and analysis. Friday, February 05 Wavelet Seminar



Speaker: Professor Jeff Hogan Department of Mathematics, University of Newcastle, Australia Title: Hypercomplex Fourier and wavelet transforms Abstract: The Clifford Fourier transform is a generalisation of the usual Fourier transform which treats multichannel signals as an algebraic whole rather than as an ensemble of one-dimensional signals. In this talk we present the basic theory of the Clifford Fourier transform and some applications to the processing of multichannel signals, especially in the two-dimensional case where the underlying algebra is that of the quaternions. Some Cliffordised versions of well-known theorems of harmonic

analysis will be presented. Tuesday, 09 Colloquium

Time: Tea: 4:00-4:30pm Talk: 4:30-5:30pm Location: Cupples I, Room 199 Host: Prof. Richard Rochberg

Speaker: Professor Alvaro Pelayo Department of Mathematics, University of California, Berkeley Title: Hamiltonian Dynamics in Symplectic and Spectral Geometry Abstract: We introduce symplectic manifolds, symplectic torus actions and integrable systems, and some of the most classical results about them. Next we will present the recent classification of symplectic 2-torus actions on 4-manifolds, and the recent classification of integrable systems on 4-manifolds for which one component of the system is peridic. Finally, we will mention and inverse spectral conjecture for this type of integrable systems and give some preliminary evidence to support it. The talk is partly based on joint works with JJ Duistermaat and S. Vu Ngoc.

Wednesdays, February 10 Graduate Organized Talks Seminar Time: 4:00-5:00pm Location: Cupples I, Room 199

Speaker: Andrew Womack Department of Mathematics, Washington University in St. Louis

Host: Raphiel Murden Title: The Posterior Predictive Information Criterion Abstract: The Posterior Predictive Information Criterion Abstract: I introduce as new information theoretic model selection criterion which can be used in any inferential setting when statistical claims are made. The method will be described in some detail, especially its theoretical underpinnings and basic properties. A simple example will be used to demonstrate the usefulness of the method. In contrast to existing methods, this fully Bayesian information theoretic approach allows one to use "vague" prior information (think frequentist estimation of parameters) as well as avoiding pitfalls like choice of parameter focus (to be explained). The talk should be accessible to all graduate students.

Thursday, February 11 Colloquium Time: Tea: 4:00-4:30pm Talk: 4:30-5:30pm Location: Cupples I, Room 199 Host: Prof. Richard Rochberg

Speaker: Professor Ravindra Girivaru Department of Mathematics, University of Missouri Title: Lefschetz theorems and the geometry of hypersurfaces Abstract: Let X and Y be algebraic manifolds (i.e. zero loci of systems of homogeneous polynomials) in projective space. If X and Y intersect ``nicely", then the codimension of the intersection Z in X is equal to the codimension of Y in projective space. Conversely, starting with a manifold X in projective space, one might ask if any submanifold Z in X of codimension k, can always be obtained as an intersection of X with a manifold Y of codimension k in the same projective space. Questions such as these and their generalisations, called Lefschetz type questions, are an attempt to capture the geometry of an arbitrary algebraic manifold X by comparing it with the ambient projective space, which is in some sense a better understood manifold. We shall start by discussing the classical case of codimension 1 subvarieties in smooth varieties where these questions are well understood. Next we move onto the case of codimension 2 subvarieties in hypersurfaces, where we show that though the geometric form of the Lefschetz theorem does not hold, an algebraic form of this theorem does. This talk will be accessible to graduate students.

Friday, February 12 Algebraic Geometry Seminar Time: 3:30-5:00pm Location: Cupples I, Room 218 Host: Prof. Mohan Kumar

Speaker: Professor Adam Ginensky WH Trading Title: Determinantal Equations for Curves and their Secant Varieties Abstract: We first prove the following: Let C be a smooth bicanonically embedded curve, then Sec^j(C) has determinantal equations iff j < Cliff(C). Examining the proof leads to a generalization of the Clifford index to an arbitrary (very ample) line bundle L. This leads to a similar theorem stating when C and it's secant varieties embedded in L \otimes L have determinantal equations. If time permits the generalizations to L_1 \otimes L_2 and a proof of the (scheme-theoretic) Eisenbud-Koh-Stillman conjecture will be discussed.

Tuesday, February 16 Colloquium Time: Tea: 4:00-4:30pm Talk: 4:30-5:30pm Location: Cupples I, Room 199 Host: Prof. Richard Rochberg

Speaker: Professor Frederic Rochon Department of Mathematics, University of Toronto Title: A cohomological formula for the index of fibred cusp operators Abstract: Fibred cusp operators are defined on a non-compact manifold with asymptotic behavior specified by a fibration at infinity. They arise naturally in various geometric contexts and in scattering theory. For such operators to be Fredholm, ellipticity is not enough. An invertibility condition at infinity must also be satisfied, making the computation of the index a subtle matter. In this talk, after reviewing the basic properties and features of fibred cusp operators, we will describe how the index of such operators can naturally be obtained by integrating a certain cohomology class, effectively providing a generalization of the Atiyah-Singer index theorem to this context.

Friday, February 19 Geometry and Topology Seminar Time: 4:00-5:00pm Location: Cupples I, Room 207 Host: Prof. Xiang Tang

Speaker: Professor Xiang Tang Department of Mathematics, Washington University in St. Louis Title: Bundles and Gerbes Abstract: In this talk, I will explain what a $G$-gerbe is. I will discuss a conjecture about duality between gerbes.

Wednesday, February 24 Minor Oral Time: 1:00-2:00pm Location: Cupples I, Room 199 Host: Prof. Renato Feres

Speaker: Jamine Ng Department of Mathematics, Washington University in St. Louis Title: Separation Cutoffs for Birth and Death Chains Abstract: Some ergodic Markov chains show a sharp transition in convergence to stationarity. This occurrence has been termed "the cutoff phenomenon," and we can ask the natural question, "when does a cutoff phenomenon exist?" In the case of

irreducible, continuous time birth and death chains that start at 0, we will show that a separation cutoff exists if and only if the product of the spectral gap and mixing time tends to infinity.

Thursday, February 25 Combinatorics Seminar Time: 12:00-1:00pm Location: Cupples I, Room 199 Host: Prof. Russ Woodroofe

Speaker: Professor Russ Woodroofe Department of Mathematics, Washington University in St. Louis Title: Erdõs-Ko-Rado theorems for simplicial complexes Abstract: A well-known result of Erdõs, Ko, and Rado states that the largest intersecting uniform family of sufficiently small sets is the family of all sets containing a fixed vertex. More recently Holroyd, Talbot, and Borg have conjectured an extension of the Erdõs-Ko-Rado Theorem for intersecting families of faces in a simplicial complex. In this talk, I will show how to use algebraic shifting to prove significant special cases of the Holroyd-Talbot/Borg Conjectures. I will give several applications to independence complexes of graphs.

Thursday, February 25 Colloquium Time: Tea: 4:00-4:30pm Talk: 4:30-5:30pm Location: Cupples I, Room 199 Host: Prof. Roya Beheshti-Zavareh

Speaker: Professor Payman Kassaei Department of Mathematics, King's College Title: What is an Eigenvariety? Abstract: In this talk, I will explain the notion of p-adic variation of automorphic forms, by starting from its simple beginnings in congruences between modular forms. I will exhibit the first instance of a p-adic family of modular forms which was employed by Serre to construct the p-adic zeta function, and go from there to more recent developments leading to Coleman-Mazur's eigencurve and more general eigenvarieties. I will also hint at how this notion could lead to a p-adic version of the Langlands philosophy.

Friday, February 26 Wavelet Seminar Time: 3:30-4:30pm Location: Cupples I, Room 199 Host: Prof. Guido Weiss

Speaker: Professor Rodolfo Torres Department of Mathematics, University of Kansas Title: The action of bilinear pseudodifferential operators on Sobolev spaces Abstract: Multilinear singular integrals arise through specific examples in the study of (para)product-like operations, commutators and other non-linear functional operations. As in the case of linear singular integrals, the analysis of the multilinear versions is intimately related to almost orthogonality estimates for the action of the operators on molecules, wavelets, and other time-frequency localized functions. In this talk we will present results about certain pseudodifferential operators than can be viewed as variable coefficient versions of the bilinear Hilbert transform. We will first review some boundedness properties on Lebesgue spaces and then focus on recent Sobolev space estimates.

Friday, February 26 Geometry and Topology Seminar Time: 4:00-5:00pm Location: Cupples I, Room 207 Host: Prof. Xiang Tang

Speaker: Professor Renato Feres Department of Mathematics, Washington University in St. Louis Title: Harmonic functions over group actions Abstract: To a group G with a given probability measure one associates a random walk on G and the class of harmonic functions, which are functions that are, in a sense, invariant under the random walk. If the group acts by homeomorphisms of a compact topological space X, one can induce a random walk on X and a concomitant notion of (continuous) harmonic function on X. Our problem is to study a dynamical Liouville property: when are continuous harmonic functions on X necessarily invariant, not just under the random walk, but under the action itself? We discuss joint work with E. Ronshausen that proves the Liouville property for actions of general countable groups on spaces of dimension 1 and gives counter examples in higher dimensions.

March 2010 - Talks Contact Marie Taris for details.

Tuesday, March 2 Algebraic Geometry Seminar Time: 4:00-5:30pm Location: Cupples I, Room 216

Host: Prof. Mohan Kumar

Speaker: Wei Deng Department of Mathematics, Washington University in St. Louis Title: Fourier-Mukai Transform and Generic Vanishing

Abstract: TBA Wednesday, March 3 Minor Oral


Host: Prof. Renato Feres

Speaker: Timothy Chumley Department of Mathematics, Washington University in St. Louis Title: Martin Boundaries and Random Walks Abstract: An introduction to discrete potential theory. We analogize the Poisson integral representation of positive harmonic functions on the disk to the realm of random walks on a discrete state space. We will use such a representation to study

the asymptotic behavior of a transient random walk. Wednesday, March 3 Graduate Organized Talks Seminar


Host: Raphiel Murden

Speaker: Safdar Quddus Department of Mathematics, Washington University in St. Louis Title: Classification of Non-commutative torus upto morita equivalence Abstract: We shall see the definition of non-commutative torus, some projections on it shall be constructed. Isomorphism of two of these torus shall be defined and we shall when two are isomorphic. Later on we shall see an equivalence relation on these torus and see when is that attained. I hope this talk be accessible to everyone with

basic functional analysis. Thursday, March 4 Minor Oral


Host: Prof. Xiang Tang

Speaker: Safdar Quddus Department of Mathematics, Washington University in St. Louis Title: Non-commutative torus, K-Theory and morita equivalence Abstract: For every irrational number we can define a non-commutative torus associated to it. We shall define it then shall see how it is different from torus, shall try to compute its K theory(K_0 and K_1). And shall classify it upto isomorphism

and morita equivalence. Thursday, March 4 Combinatorics Seminar

Time: 12:00-1:00pm Location: Cupples I, Room 199 Host: Russ Woodroofe

Speaker: Cindy Traub Department of Mathematics, Southern Illinois University Title: The computational complexity of optimal redistricting Abstract: Measurements in population shifts from the US census dictate whether existing boundaries of political districts will change or remain the same. The drawing of these boundaries are governed by a complex mix of rules describing "fairness", and the actual drawing is often left to the party with majority representation. We will examine a result of Puppe and Tasnadi that proves optimal partisan redistricting with geographical constraints to be NP-Complete.

Tuesday, March 16 Algebraic Geometry Seminar Time: 4:00-5:30pm Location: Cupples I, Room 216 Host: Prof. Mohan Kumar

Speaker: Prof. Roya Beheshti-Zavareh Department of Mathematics, Washington University in St. Louis Title: A Characterization of Rationally Connected Varieties Abstract: TBA

Wednesday, March 17 Graduate Organized Talks Seminar Time: 4:00-5:00pm Location: Cupples I, Room 199 Host: Raphiel Murden

Speaker: Michael Deutsch Department of Mathematics, Washington University in St. Louis Title: Minimal curves and the spinor representation Abstract: Suppose we have a curve. We want to compute its curvature at a point. We can construct the Frenet frame, right? Not if its minimal! Cartan considered (and solved) the problem of determining curvature of parameterized complex curves in C^3 whose tangent vector has "zero length." We will present a slick spin-geometric approach to Cartan's problem which we think makes the notion of curvature in this context actually understandable.

Friday, March 19 Colloquium Time: Tea: 3:30-4:00pm Talk: 4:00-5:00pm Location: Cupples I, Room 199 Host: Prof. Nan Lin

Speaker: Professor Yazhen Wang Department of Mathematics, University of Wisconsin at Madison Title: Modeling and Analyzing High-Frequency Financial Data Abstract: Volatilities of asset returns are central to the theory and practice of asset pricing, portfolio allocation, and risk management. In financial economics, there is extensive research on modeling and forecasting volatility up to the daily level based on Black-Scholes, diffusion, GARCH, stochastic volatility models and implied volatilities from option prices. Nowadays, thanks to technological innovations, high-

frequency financial data are available for a host of different financial instruments on markets of all locations and at scales like individual bids to buy and sell, and the full distribution of such bids. The availability of high-frequency data stimulates an upsurge interest in statistical research on better estimation of volatility. This talk will start with a review on low-frequency financial time series and high-frequency financial data. Then I will introduce popular realized volatility computed from high-frequency financial data and present my work on analyzing jump and volatility variations and estimating volatility matrices of large size.

Friday, March 19 Geometry and Topology Seminar Time: 4:00-5:00pm Location: Cupples I, Room 207 Host: Prof. Xiang Tang

Speaker: Rajan Mehta Department of Mathematics, Washington University in St. Louis Title: Adjoint superrepresentations of a Lie groupoid Abstract: Lie groupoids are a generalization of Lie groups that incorporate both "internal" and "external" symmetries. Representation theory is a valuable tool for studying Lie groups, so it would be nice to similarly utilize representation theory in the study of Lie groupoids. There is a reasonably natural definition of Lie groupoid representation, but it unfortunately fails to include an adjoint representation. However, it turns out that this problem can be averted if we allow for the more general notion of "superrepresentation". Although the adjoint superrepresentations are not canonical, they all arise as manifestations of something that is canonical. I will describe this canonical object and sketch how superrepresentations can be produced from it.

Tuesday, March 23 Algebraic Geometry Seminar Time: 4:00-5:30pm Location: Cupples I, Room 216 Hosts: Prof. Mohan Kumar

Speaker: Professor Adrian Clingher Department of Mathematics, University of Missouri, St. Louis Title: Special Two-Isogenies on K3 Surfaces Abstract: Let Z be the minimal resolution of a double cover of the projective plane branched over six distinct lines. The surface Z is a K3 surface with Picard rank 16 or higher. I will describe a special involution of Z that determines a two-isogeny of K3 surfaces.

Wednesday, March 24 Colloquium Time: Tea: 3:00-3:30pm Talk: 3:30-4:30pm Location: Cupples I, Room 199 Host: Prof. Quo-Shin Chi

Speaker: Professor Reiko Miyaoka Department of Mathematics, Tohoku University Title: Isoparametric hypersurface theory and its applications Abstract: Starting with an introduction, I will mention the latest results on the classification problem of the isoparametric hypersurfaces. Also, I'd like to talk about the relations with special manifolds, calibrated submanifolds, and a few other topics.

Thursday, March 25 Senior Honor Thesis Presentation Time: 10:00-11:00am Location: Cupples I, Room 199 Hosts: Prof. Ronald Freiwald

Speaker: Andrew Wilson Department of Mathematics, Washington University in St. Louis Title: Explorations of a Generalization of the Descent Statistic Abstract: In his recent PhD thesis, Denis Chebikin defined a number of variations on the standard notions of descents and inversions from the theory of permutations. One of these variations is a generalization of the descent statistic. Traditionally, a permutation is said to have a descent at position i if its value at position i is greater than its value at position i+1. In the generalized form proposed by Chebikin, a permutation is said to have a k-descent at position i if the subsequence of length k beginning at position i has an odd relative ordering. In this paper, we explore two properties of this generalization that have not yet been addressed by Chebikin. First, we aim to calculate exactly how many permutations have a certain descent set. We are able to calculate these values for k = n-1 and k = n-2, and we state some ideas about the general case. Second, we attempt to understand how the Solomon descent algebra functions in relation to the new concept of descents. Specifically, when k = n-1, we see that, if we assume the descent algebra exists, it has an interesting structure, but when k = n-2, we find that the traditional descent algebra does not exist.

Thursday, March 25 Combinatorics Seminar Time: 12:00-1:00pm Location: Cupples I, Room 199 Hosts: Russ Woodroofe

Speaker: Rajan Mehta Department of Mathematics, Washington University in St. Louis Title: Simplicial sets, groups, and the resulting insanity Abstract: I will review the "nerve" construction, which provides a way to construct the classifying space of a group as a simplicial set. One of the interesting features of this construction is that it is in some sense reversible--any simplicial set satisfying certain properties is the classifying space of a group. If you look at this statement the right way, you may even be led to the scandalous conclusion that "simplicial set satisfying certain properties" is the right way to *define* a group. And if you're feeling brazen, you might think to tweak those properties and see what happens. Go ahead and do it, I dare you.

Thursday, March 25 Taibleson Lecture

Time: Tea: 4:00-4:30pm Talk: 4:30-5:30pm Location: Cupples I, Room 199 Hosts: Profs. Al Baernstein, Guido Weiss

Speaker: Professor Rodrigo Bañuelos Department of Mathematics, Purdue University Title: Lévy processes and Fourier multipliers Abstract: Martingales arising from Brownian motion can be used to study properties of several classical Fourier multipliers, including the Hilbert transform, the Riesz transforms (and their Gaussian versions) and the Beurlin-Ahlfors operator. In this lecture we will explore similar techniques where stochastic integrals with respect to Brownian motion are replaced by similar quantitites arising from Lévy processes. This approach leads to a class of Fourier (Lévy) multipliers for which one gets $L^p$ estimates that are similar to those obtained for the above mentioned singular integrals.

Friday, March 26 Geometry and Topology Seminar Time: 4:00-5:00pm Location: Cupples I, Room 207 Hosts: Prof. Xiang Tang

Speaker: Professor Hongkun Zhang Department of Mathematics and Statistics, University of Massachusetts Amherst Title: Spectral gaps of transfer operators for billiards Abstract: In this talk I will first introduce classical billiards, which originated from the Boltzman-Sinai's Ergodic Hypotheses. For chaotic billiards, the system-generated stochastic processes has exponential decay of correlations if the transfer operator has a spectral gap (at 1). It was shown that there are many types of classical billiards including the Bunimovich Stadium and billiards with cusps that only have slow decay of correlations. As a result, there are no spectral gaps for these systems. On the other hand, for a class of random billiards that is the subject of this talk, we are able to show that their transfer operators, or Markov operators have a positive spectral gap even if the boundary of the billiard cell contains arcs and cusps. Furthermore we are able to relate the gap and the curvatures of the boundary. This talk is based on a joint work with Renato Feres.

April 2010 - Talks Contact Marie Taris for details.

Thursday, April 1 Combinatorics Seminar Time: 12:00-1:00pm Location: Cupples I, Room 199


Speaker: Rajan Mehta Department of Mathematics, Washington University in St. Louis Title: Simplicial sets, groups, and the resulting insanity, Part II Abstract: I will review the "nerve" construction, which provides a way to construct the classifying space of a group as a simplicial set. One of the interesting features of this construction is that it is in some sense reversible--any simplicial set satisfying certain properties is the classifying space of a group. If you look at this statement the right way, you may even be led to the scandalous conclusion that "simplicial set satisfying certain properties" is the right way to *define* a group. And if you're feeling brazen, you might think to tweak those properties and see what happens. Go

ahead and do it, I dare you. Thursday, April 1 Colloquium

Time: Tea: 3:30-4:00pm Talk: 4:00-5:00pm Location: Cupples I, Room 199

Host: Prof. Nan Lin

Speaker: Professor Sid Chib Onlin Business School, Washington University in St. Louis Title: Dealing with the Compliance Problem in Randomized Trials Abstract: In randomized trials with human subjects, compliance with the assigned treatment is often less than perfect and, because of the concern that the lack of compliance is due to observed and unobserved confounders, the trial takes on the features of an observational study. One goal of the analysis now is to find the causal effect of the intake, instead of the causal effect of the assignment. We present some Bayesian ways of finding this causal effect and illustrate the ideas in a toy example

and a more substantial real data example. Friday, April 2 Geometry and Topology Seminar

Time: 4:00-5:00pm Location: Cupples I, Room

Speaker: Professor Xiang Tang Department of Mathematics, Washington University in St. Louis

207

Host: Prof. Xiang Tang Title: Let $G$ be a finite group and $Y$ a $G$-gerbe over an orbifold $B$. We will explain a construction of a new orbifold $\widehat{Y}$ and a flat $U(1)$-gerbe $c$ on $\widehat{Y}$. Motivated by a proposal in physics, we study a mathematical duality of $G$-gerbes, which asserts that the geometry of $Y$ is equivalent to the geometry of $\widehat{Y}$ twisted by $c$. The Mackey machine provides us the right tool to study such a problem. We will discuss some results in symplectic topology with the help of noncommutative geometry. This is a joint work with Hsian-

hua Tseng. Thursday, April 8 Combinatorics Seminar


Hosts: Prof. Russ Woodroofe

Speaker: Professor Erin Chambers Department of Mathematics, St. Louis University Title: On the Height of a Homotopy Abstract: Given 2 homotopic curves in a topological space, there are several ways to measure similarity between the curves, including Hausdorff distance and \Frechet distance. In this talk, we examine a different measure of similarity which considers the family of curves represented in the homotopy between the curves, and measures the longest such curve, known as the {\em height} of the homotopy. In other words, if we have two homotopic curves on a surface and view a homotopy as a way to morph one curve into the other, we wish to find the longest intermediate curve along the morphing. Our model assumes we are given a pair of disjoint embedded homotopic curves (where the endpoints remained fixed over the course of the homotopy) in an edge-weighted planar triangulation satisfying the triangle inequality. Our conjecture is that the homotopy with minimum height never makes a ``backwards" move and results in disjoint simple intermediate curves; here, we examine several properties of a minimum height homotopy which may prove useful in proving such a fact.

This is joint work with David Letscher that appeared in CCCG 2009. Thursday, April 8 Colloquium

Time: Tea: 4:00-4:30pm Talk: 4:30-5:30pm Location: Cupples I, Room 199

Hosts: Prof. Quo-Shin Chi

Speaker: Professor Yng-Ing Lee Department of Mathematics, National Taiwan University Title: Soliton Solutions for Lagrangian Mean Curvature Flow Abstract: The mean curvature vector points in the direction in which the volume decreases most rapidly and mean curvature flow deforms the submanifold in the direction of the mean curvature vector. However, finite-time singularities may occur along the flow. In geometric flows such as Ricci flow or mean curvature flow, singularities are often locally modeled on soliton solutions. In the case of mean curvature flows, two types of soliton solutions of particular interest are those moved by scaling or translation in Euclidean space. They play an important role in understanding singularities. When the initial submanifold is Lagrangian in a Kahler-Einstein manifold, the smooth solution of the mean curvature flow will still be Lagrangian. In this talk, I will report some of my work on Lagrangian soliton solutions with different properties and particularly emphasize those examples related to Schoen-Wolfson cones that appear to be an obstruction to the existence of special Lagrangian surfaces. The results presented in this talk consist of two papers with Mu-Tao Wang, and a paper with

Dominic Joyce and Mao-Pei Tsui. Friday, April 9 Geometry and Topology Seminar

Time: Talk: 4:00-5:00pm Location: Cupples I, Room 207

Hosts: Prof. Quo-Shin Chi

Speaker: Professor Yng-Ing Lee Department of Mathematics, National Taiwan University Title: The Existence of Hamiltonian Stationary Lagrangians Abstract: Hamiltonian stationary Lagrangians are Lagrangian submanifolds that are critical points of the area functional under Hamiltonian deformations. They are generalizations of special Lagrangians. We show the existence of many compact Hamiltonian stationary Lagrangians in every compact symplectic manifold with a compatible metric. A local criterion in Kahler manifolds where a family of Hamiltonian stationary Lagrangian tori can be found is also derived. The first result

is a joint work with Joyce and Schoen. Monday, April 12 Thesis Defense

Time: 3:30-5:00pm Location: Cupples I, Room 199 Hosts: Prof. Gary Jensen

Speaker: Michael Deutsch Department of Mathematics, Washington University in St. Louis Title: Equivariant deformations of horospherical surfaces Abstract: We reinterpret the classical Goursat transform on minimal surfaces as conformal transformation of the Gauss map, thereby allowing us to deform these surfaces for various geometric purposes. This deformation has a simple analogue for CMC1 surfaces which, when properly defined, makes the Goursat transform equivariant with respect to the Lawson correspondence, all of which is introduced in

a quaternionic upper-half space model, designed just for this purpose. Time permitting, we indicate a compelling analogy between (a) the Goursat transformation law and integrability conditions for the ``spin curve'' of a horospherical surface, and (b) the Lorentz transformation law and equations of motion for the spin wavefunction of a free massless particle.

Monday, April 12 Analysis Seminar Time: 4:00-5:00pm Location:Cupples I, Room 207 Hosts: Prof. Richard Rochberg

Speaker: Kabe Moen Department of Mathematics, Washington University in St. Louis Title: Sharp weighted bounds for classical operators Abstract: We will discuss weighted inequalities for classical operators in harmonic analysis. The operators include: maximal operators, fractional integral operators, singular integrals and variants of these. All of these operators are bounded on weighted Lebesgue spaces when the weight belongs to a certain class of weights known as A_p. We examine the sharp dependence on the operator norms and the A_p constant of the weight.

Tuesday, April 13 Algebraic Geometry Seminar Time: 4:00-5:30pm Location:Cupples I, Room 216 Hosts: Prof. Mohan Kumar

Speaker: G.V. Ravindra Department of Mathematics, University of Missouri, St. Louis Title: Multiplier Ideals Abstract: TBA

Wednesday, April 14 Special Joint Mathematics-Physics Colloquium Time: Tea: 3:15pm in Cupples I, Room 199; Talk: 4:00-5:00pm Location: Crow, Room 204 Hosts: Profs. David Wright, Ken Kelton, Ram Cowsik

Speaker: Professor Srinivasa Varadhan, 2007 recipient of the Abel Prize Courant Institute of Mathematical Sciences, New York University Title: Large Deviations, theory and examples Abstract: The theory of large deviations is ubiquitous and plays both a direct and indirect role in many applications. Entropy in some form is a basic ingredient. We will review the basic theory and illustrate some of the applications.

Thursday, 15 Major Oral Time: 1:00-2:30pm Location: Cupples I, Room 207 Host: Prof. Renato Feres

Speaker: Jasmine Ng Department of Mathematics, Washington University in St. Louis Title: The Cutoff Phenomenon for Ergodic Markov Processes Abstract: The cutoff phenomenon was first introduced in the context of ergodic finite Markov chains, but we can also consider it in the context of ergodic Markov processes. A natural question to ponder is whether or not we can prove that a cutoff phenomenon exists without examining the problem in excruiating detail and, in particular, determining the cutoff time. The answer to this question is yes, and we will show the existence of a cutoff depends only on a simple criterion involving the spectral gap and mixing time. Moreover, we will consider an example involving Brownian motion on compact Riemannian manifolds.

Thursday, April 15 Colloquium Time: Tea: 4:00-4:30pm Talk: 4:30-5:30pm Location: Cupples I, Room 199 Host: Prof. Al Baernstein

Speaker: Professor Terry Sheil-Small Department of Mathematics, University of York, England Title: An extremal problem for non-vanishing functions on Bergman space Abstract: Click here.

Tuesday, April 20 Thesis Defense Time: 10:00am-12:00pm Location: Cupples I, Room 199 Host: Prof. Richard Rochberg

Speaker: Nicholas Sedlock Department of Mathematics, Washington University in St. Louis Title: Multiplication of Truncated Toeplitz Operators Abstract: We discuss the multiplication of truncated Toeplitz operators (or TTOs) on backward shift invariant subspaces of the Hardy space of the unit disc. Specifically we discuss when the product of two TTOs is itself a TTO, finding an equivalent to a similar result of Brown and Halmos for ordinary Toeplitz operators. This leads us to investigate the commutants of certain rank-one perturbations of the compressed shift operator, deriving a symbol calculus for TTOs, as well as several other results.

Tuesday, April 20 Algebraic Geometry Seminar Time: 4:00-5:30pm Location: Cupples I, Room 199 Host: Prof. Mohan Kumar

Speaker: Professor Mohan Kumar Department of Mathematics, Washington University in St. Louis Title: Multiplier Ideals (Cont.) Abstract: TBA

Wednesday, April 21 Department Awards Ceremony Time: Tea: 4:00-4:30pm Talk: 4:30-5:30pm Location: Room 199 Host: Prof. Ronald Freiwald

Awards to mathematics faculty, graduate students, undergraduate students, ... , and more.

Thursday, April 22 Combinatorics Seminar Time: 12:00-1:00pm Location: Cupples I, Room 199 Host: Russ Woodroofe

Speaker: Russ Woodroofe Department of Mathematics, Washington University in St. Louis Title: Regularity of graphs Abstract: The Castelnuovo-Mumford regularity is an important invariant in commutative algebra. I'll define the regularity of a graph through its edge ideal, interpret the regularity in terms of the topology of the independence complex, and give various bounds coming from the combinatorics of the graph.

Thursday, April 22 Colloquium Time: 1:00-2:00pm Location: Cupples I, Room 199 Hosts: Profs. Jeff Gill and David Wright

Speaker: Minjung Kyung Department of Statistics, University of Florida Title: Penalized Regression, Standard Errors, and Bayesian Lassos Abstract: Penalized regression methods for simultaneous variable selection and coefficient estimation, especially those based on the lasso of Tibshirani (1996), have received a great deal of attention in recent years, mostly through frequentist models. Properties such as consistency have been studied, and are achieved by different lasso variations. Here we look at a fully Bayesian formulation of the problem, which is flexible enough to encompass most versions of the lasso that have been previously considered. The advantages of the hierarchical Bayesian formulations are many. In addition to the usual ease-of-interpretation of hierarchical models, the Bayesian formulation produces valid standard errors (which can be problematic for the frequentist lasso), and is based on a geometrically ergodic Markov chain. We compare the performance of the Bayesian lassos to their frequentist counterparts using simulations, data sets that previous lasso papers have used, and a difficult modeling problem for predicting the collapse of governments around the world. In terms of prediction mean squared error, the Bayesian lasso performance is similar to and, in some cases, better than, the frequentist lasso.

Thursday, April 22 Loeb Undergraduate Lecture in Mathematics

Time: Tea: 3:45-4:30pm, Cupples I, Room 200 Talk: 4:30-5:30pm Location: January Hall, Room 110 Host: Prof. Ronald Freiwald

Speaker: Professor Martin Golubitsky Department of Mathematics and Director of the Mathematical Biosciences Institute, Ohio State University Title: Symmetries and Animal Gaits Abstract: Many gaits of four-legged animals can be described by spatio- temporal symmetries. For example, when a horse paces it moves both left legs in unison and then both right legs and so on. The motion is described by two symmetries: Interchange front and back legs, and swap left and right legs with a half-period phase shift. Biologists postulate the existence of a central pattern generator (CPG) in the neuronal system that sends periodic signals to the legs. CPGs can be thought of as electrical circuits that produce periodic signals and can be modeled by coupled systems of differential equations with symmetries based on leg permutation. In this lecture we discuss animal gaits; describe how periodic solutions with prescribed spatio- temporal symmetry can be formed in symmetric systems; construct a CPG architecture that naturally produces quadrupedal gait rhythms; and make several testable predictions about gaits.

Friday, April 23 Geometry and Topology Seminar Time: 4:00-5:00pm Location: Cupples I, Room 207 Host: Prof. Xiang Tang

Speaker: Professor Larry Conlon Department of Mathematics, Washington University in St. Louis Title: Surface automorphisms after Nielsen-Thurston and Handel-Miller Abstract: The Nielsen-Thurston theory classifies the isotopy classes of automorphisms of compact surfaces of negative Euler characteristic, using geodesic laminations of these surfaces. The most important class is represented by pseudo-Anosov automorphisms. While this theory is an important part of low dimensional topology, geometry and dynamical systems, and is well documented in the literature, it is not well understood by many geometers and topologists. I will give a detailed sketch. The Handel-Miller theory is a loosely analogous classification of end-periodic automorphisms of noncompact surfaces, also an important topic, but nowhere adequately documented. As time permits, I will also sketch this. John Cantwell and I have written a detailed account of the Handel-Miller theory and are applying it to the analysis of finite depth foliations in 3-manifolds. It has also been applied by Sergio Fenley to see how the leaves of depth one foliations of hyperbolic 3-manifolds limit on the sphere at infinity. This was analogous to, but with surprising different features from, the Cannon-Thurston study of the fibers of a fibration of a hyperbolic 3-manifold over the circle.

Monday, April 26 Colloquium CANCELLED Time: 1:00-2:00pm

CANCELLED Speaker: Xin Qi

Location: Cupples I, Room 199 Host: Profs. Jeff Gill and David Wright

Department of Epidemiology and Public Health, School of Medicine, Yale University Title: Functional principal component analysis for discretely observed random functions Abstract: We propose a new method for functional principal component analysis for discretely random functions by solving successive optimization problems. We consider two different settings for designs of the observation points: regular case and irregular case. Our method do not need the assumptions that sample curves or covariance functions are smooth. Hence, our method can be applied to many important models or processes with nonsmooth sample curves or nonsmooth convariance functions. Our methods can tune the smoothness for estimations of different principal components separately which increases the flexibility. We apply our method to simulated and real data. We give the consistency of our method.

Tuesday, April 27 Colloquium Time: 3:00-4:00pm Location: Cupples I, Room 199 Host: Profs. Jeff Gill and David Wright

Speaker: Yeojin Chung Department of Statistics, PennState Title: Likelihood-tuned Density Estimation and its Application to Clustering Abstract: We consider an improved multivariate nonparametric density estimator which arises from treating the kernel density estimator as an element of the model that consists of all mixtures of the kernel, continuous or discrete. One can obtain the kernel density estimator with "likelihood-tuning" by using the uniform density as the starting value in an EM algorithm. The second tuning leads to a fitted density with higher likelihood than the kernel density estimator. A penalized version of the likelihood-tuning gives the kernel density estimator with t-kernel with the first tuning. The second penalized-tuning leads to a density estimator with local shape adaptation in the t-kernel function. We compare the performance of the new density estimators with other improved density estimators and apply them to model-based clustering.

Tuesday, April 27 Algebraic Geometry Seminar Time: 4:00-5:30pm Location: Cupples I, Room 199 Host: Prof. Mohan Kumar

Speaker: Professor Mohan Kumar Department of Mathematics, Washington University in St. Louis Title: Multiplier Ideals (Cont.) Abstract: TBA

Wednesday, April 28 Statistics Seminar Time: 4:30-5:30pm Location: Cupples I, Room 199 Host: Prof. Nan Lin

Speaker: Professor Edward Bedrick Department of Mathematics and Statistics, University of New Mexico Title: See Statistics Seminar Schedule Abstract: See link above.

Thursday, April 29 Combinatorics Seminar CANCELLED Time: 12:00-1:00pm Location: Cupples I, Room 199 Host: Russ Woodroofe

CANCELLED Speaker: Cindy Traub Department of Mathematics, Southern Illinois University at Edwardsville Title: TBA Abstract: TBA

Thursday, April 29 Major Oral Time: 1:00-2:30pm Location: Cupples I, Room 207 Host: Prof. Renato Feres

Speaker: Timothy Chumley Department of Mathematics, Washington University in St. Louis Title: Discretization of Positive Harmonic Functions on Riemannian Manifolds Abstract: Given a so-called *-recurrent discrete subset X of a Riemannian manifold M, we outline a procedure for discretizing Brownian motion on M into a Markov chain on X in such a way that positive harmonic functions for the Laplace-Beltrami operator on M restrict to harmonic functions for the discrete Laplacian on X.

Thursday, April 29 Roever Colloquium Time: Tea: 4:00-4:30pm Talk: 4:30-5:30pm Location: Cupples I, Room 199 Host: Prof. Quo-Shin Chi

Speaker: Professor Simon Brendle Department of Mathematics, Stanford University Title: Curvature, sphere theorems, and the Ricci flow Abstract: In 1926, Hopf proved that any compact, simply connected Riemannian manifold with constant curvature 1 is isometric to the standard sphere. Motivated by this result, Hopf posed the question of whether a compact, simply connected manifold with suitably pinched curvature is topologically a sphere. This question has been studied by many authors over the past six decades, a milestone being the Topological Sphere Theorem proved by Berger and Klingenberg in 1960. In this lecture, I will discuss the history of this problem, and describe the proof (joint with R. Schoen) of the Differentiable Sphere Theorem. This theorem classifies all manifolds with 1/4-pinched curvature up to diffeomorphism. The distinction between homeomorphism and diffeomorphism is significant in light of the exotic spheres constructed by Milnor; the proof uses the Ricci flow technique introduced by

Hamilton. Friday, April 30 Roever Seminar

Time: 3:00-4:00pm Location: Cupples II, Room 217 Host: Prof. Quo-Shin Chi

Speaker: Professor Simon Brendle Department of Mathematics, Stanford University Title: Blow-up phenomena for the Yamabe equation Abstract: The Yamabe problem asserts that any Riemannian metric on a compact manifold can be conformally deformed to one of constant scalar curvature. However, this metric is not, in general, unique, and there are examples of manifolds that admit many metrics of constant scalar curvature in a given conformal class. It was conjectured by R. Schoen in the 1980s (and later by Aubin) that the set of all metrics of constant scalar curvature 1 in a given conformal class is compact, except if the underlying manifold is conformally equivalent to the sphere $S^n$ equipped with its standard metric. I will discuss counterexamples to this conjecture in dimension 52 and higher. I will also describe joint work with F. Marques, which extends these counterexamples to dimension 25 and higher. The condition $n \geq 25$ turns out to be optimal.

May 2010 - Talks Contact Marie Taris for details.

Monday, May 3 Colloquium Time: 2:30-4:00pm Location: Cupples I, Room 199 Host: Profs. Jeff Gill and David

Wright

Speaker: Xin Qi Department of Epidemiology and Public Health, School of Medicine, Yale University Title: Functional principal component analysis for discretely observed random functions Abstract: We propose a new method for functional principal component analysis for discretely random functions by solving successive optimization problems. We consider two different settings for designs of the observation points: regular case and irregular case. Our method do not need the assumptions that sample curves or covariance functions are smooth. Hence, our method can be applied to many important models or processes with nonsmooth sample curves or nonsmooth convariance functions. Our methods can tune the smoothness for estimations of different principal components separately which increases the flexibility. We apply

our method to simulated and real data. We give the consistency of our method. Thursday, May 6 Combinatorics Seminar

RESCHEDULED, see 05/07/2010 Time: 12:00-1:00pm Location: Cupples I, Room 199


Speaker: Jay Schweig Department of Mathematics, University of Kansas, Lawrence Title: On lattice path matroids and polymatroids

Abstract: TBA

Thursday, May 06 Colloquium Time: Tea: 4:00-4:30pm Talk: 4:30-5:30pm Location: Cupples I, Room 199


Speaker: Professor Maciej Paluszynski Department of Mathematics, University of Wrocal Title: TBA

Abstract: TBA Friday, May 7 Combinatorics Seminar



Speaker: Jay Schweig Department of Mathematics, University of Kansas, Lawrence Title: On lattice path matroids and polymatroids Abstract: Lattice path matroids are an especially tractable class of transversal matroids whose bases are in correspondence with planar lattice paths. We discuss

some enumerative properties of these matroids, one of which leads naturally to a related class of discrete polymatroids. We then examine these polymatroids and their toric ideals. Finally, we provide generating sets and Gr\"obner bases for these ideals, and discuss many possible directions for future research. No previous knowledge of matroid theory or toric ideals will be assumed.

Wednesday, May 19 Thesis Defense Time: 3:30-4:30pm Location: Cupples I, Room 199 Host: Prof. Stanley Sawyer

Speaker: Ji Yan Department of Mathematics, Washington University in St. Louis Title: Maternal Smoking Cessation and Infant Birth Weight: New Evidence from a UK Cohort Data Abstract: This thesis provides new evidence on the deadline by which pregnant mothers should quit smoking to nullify the negative impact of smoking on infant birth weight. I use a large UK cohort data to find the babies whose mother stop smoking in the first three months are as heavy as those of nonsmokers. In particular, the fourth month of pregnancy turns to be an important threshold when smoking in this stage will significantly reduce infant birth weight, in contrast to the negligible effect due to prenatal smoking in any month of the first trimester. These results are robust to both a series of principle competent analyses that reduce the dimensions of other important covariates for infant birth weights, and different model selection procedures.

August 2010 - Talks Contact Marie Taris for details.

Wednesday, August 18 Major Oral Time: 10:00-11:30am Location: Cupples I, Room199 Host: Prof. Xiang Tang

Speaker: Safdar Quddus Department of Mathematics, Washington University in St. Louis Title: Cyclic Cohomology of some algebras Abstract: We shall define hochschild homology and then cyclic homology, and then shall Insha'Allah provide a way to compute cyclic cohomology using a long exact sequence. We shall Insha'Allah do the computation for algebra of smooth functions on a manifold and then Insha'Allah on the irrational rotational algebra.

Tuesday, August 24 Thesis Defense Time: 2:00-4:00pm Location: Cupples I, Room199 Host: Prof. Stanley Sawyer

Speaker: Xiao Huang Department of Mathematics, Washington University in St. Louis Title: Using Dirichlet Process prior for Bayesian mixture clustering Abstract: We describe a non-parametric Bayesian model using genotype data to classify individuals among populations while the total number of populations is unknown. The model assumes that a population is characterized by a set of allele frequencies which follow multinomial distributions. The Dirichlet Process is applied as the prior distribution. The method estimate the number of populations together with the allele frequencies and the ancestry coefficient of each individual. Distance matrices based on MCMC runs are generated to create a phylogeny of the ancestral populations.

Friday, August 27 Analysis Seminar Time: 9:30-10:30am Location: Eads, Room 112 Host: Prof. Nik Weaver

Speaker: Professor Andrew Toms Department of Mathematics and Statistics, York University Title: Classification and C*-algebras Abstract: What does it mean to classify a category of objects? This talk will explore two approaches through the lens of C*-algebra theory: complete invariants and Borel complexity. On the invariant side, we will trace the history of the classification of C*-algebras by K-theory, starting with the seminal work of Glimm and arriving at George Elliott's classification functor formalism. On the other hand, we will discuss the idea of Borel reducibility, machinery from the world of descriptive set theory meant to quantify how difficult it is to assign invariants to isomorphism classes of a category in a computable way. Finally, we'll see examples

of interaction between these two approaches, where a classification by invariants leads to new results on the Borel complexity of nuclear separable C*-algebras.

September 2010 - Talks Contact Marie Taris for details.

Thursday, September 2 Colloquium CANCELLED. Rescheduled: see 09/09/2010 Time: Tea: 4:00-4:30pm Talk: 4:30-5:30pm Location: Cupples I, Room 199 Host: Prof. Nik Weaver

Speaker: Professor David Sherman Department of Mathematics, University of Virginia Title: Model theory for functional analysis Abstract: Model theory studies the interplay between mathematical structures and their logical properties. Some of its most beautiful theorems involve a construction called an \textit{ultrapower}. Many standard objects in functional analysis, such as Banach spaces and operator algebras, carry useful notions of ultrapower, but this does not interact well with classical model theory. An elegant recent solution, very natural for analysts, is to switch to a logic in which truth values are drawn from the interval [0,1]. I will give a ``big picture" survey of this approach and its prehistory, not assuming that the audience has any familiarity with logic or ultrapowers.

Thursday, September 9 Geometry and Topology Seminar Time: 3:00-4:00pm Location: Eads, Room 116 Host: Prof. Xiang Tang

Speaker: Professor Xiang Tang Department of Mathematics, Washington University in St. Louis Title: Introduction

Thursday, September 9 Colloquium Time: Tea: 4:00-4:30pm Talk: 4:30-5:30pm Location: Cupples I, Room 199 Host: Prof. Nik Weaver

Speaker: Professor David Sherman Department of Mathematics, University of Virginia Title: Model theory for functional analysis Abstract: Model theory studies the interplay between mathematical structures and their logical properties. Some of its most beautiful theorems involve a construction called an \textit{ultrapower}. Many standard objects in functional analysis, such as Banach spaces and operator algebras, carry useful notions of ultrapower, but this does not interact well with classical model theory. An elegant recent solution, very natural for analysts, is to switch to a logic in which truth values are drawn from the interval [0,1]. I will give a ``big picture" survey of this approach and its prehistory, not assuming that the audience has any familiarity with logic or ultrapowers.

Monday, September 13 Analysis Seminar Time: 4:00-5:00pm Location: Cupples I, Room 199 Host: Prof. John McCarthy

Speaker: Professor John McCarthy Department of Mathematics, Washington University in St. Louis Title: Organizational Meeting

Tuesday, September 14 Minor Oral Time: 12:00-1:00pm Location: Cupples I, Room 199 Host: Prof. John Shareshian

Speaker: Marina Dombrovskaya Department of Mathematics, Washington University in St. Louis Title: Invariants of Finite Groups Abstract:Invariant theory combines in itself seemingly different areas of mathematics: group theory, commutative algebra, and combinatorics. Not only invariant theory is quite an interesting subject of study by itself, but it also has many applications in other areas of mathematics including algebraic geometry, algebraic topology and combinatoris. In this talk we will introduce the notion of a ring of invariants under a finite group action and describe some very interesting algebraic and combinatorial properties of such a ring, including properties of generators, Molien series and when invariant ring is Cohen-Macaulay. We will also talk about Shepard-Todd-Chevalley Theorem, which completely describes the structure of invariant rings of (pseudo) reflection groups, and give some combinatorial applications of invariant theory. This talk will mostly follow paper by R. Stanley "Invariants of Finite Groups and Their Applications".

Tuesday, September 14 Math Club Time: 5:30-6:30pm Location: Cupples I, Room 199 Host: Prof. John McCarthy

Movie: Good Will Hunting

Wednesday, September 15 Algebraic Geometry Seminar

Time: 1:30-3:00pm Location: Eliot, Room 103 Host: Prof. Mohan Kumar

Speaker: Professor Charles Doran Department of Mathematics, University of Alberta and the Pacific Institute for the Mathematical Sciences Title: Variations of Hodge structure from Calabi-Yau moduli: A progress report Abstract:John Morgan and I classified the weight three variations of Hodge structure over the thrice punctured sphere which could arise from families of Calabi-Yau threefolds with h^{2,1}=1. Some puzzles remained, however, regarding actual geometric realization of such families. In this talk I'll provide a progress report on the search for these Calabi-Yau manifolds. A special role is played by geometric transitions.


Speaker: Professor Heather Dye Department of Mathematics, McKendree University Title: Categorifications of the Arrow Polynomial Abstract: Will present several categorifications of the arrow polynomial, an invariant of virtual links. An overview of virtual links, the arrow polynomial, and Khovanov homology will be included.


Speaker: Professor John McCarthy Department of Mathematics, Washington University in St.Louis Title: Ando Inequalities for non-commuting matrices

Monday, September 20 Graduate Seminar Time: 5:00-6:00pm Location: Cupples I, Room 199 Host: Prof. Ed Spitznagel

Speaker: Andrew Womack Department of Mathematics, Washington University in St.Louis Title: Bayesian Model Selection via Renyi Entropies Abstract: Hypothesis testing and point (interval) estimation are perhaps the most important parts of any statistical analysis. Under certain assumptions, there is a coherent way to perform both objectives at once. A minimal relaxation of these assumptions leads to (modern) fiducial point estimation. However, there is no reasonable theory of fiducial hypothesis testing. Presented is a (very large) family of information criteria which provide tools to perform fiducial model selection. The criteria presented are modifications of the classical Bayes Factor (the probability that a model is true) by Renyi entropies. From a fiducial point of view, these criteria are desirable because they allow the use of non-finite measures. These criteria naturally contain the Bayes Factor as a special case and provide analogues of two methods for trying to perform with fiducial model selection (the intrinsic and fractional methods). I will present the necessary background to understand the motivation behind the family of criteria and present a few examples.

Wednesday, September 22 Algebraic Geometry Seminar Time: 4:00-5:30pm Location: Cupples I, Room 207 Host: Prof. Mohan Kumar

Speaker: Professor G.V. Ravindra Department of Mathematics, University of Missouri, St.Louis Title: The Picard-Lefschetz formula and a conjecture of Kato: the case of Lefschetz fibrations

Wednesday, September 22 Combinatorics Seminar: Major Oral Time: 4:00-5:00pm Location: Cupples I, Room 199 Hosts: Prof. John Shareshian & Russ Woodroofe

Speaker: Marina Dombrovskaya Department of Mathematics, Washington University in St.Louis Title: Quadratic and cubic invariants of unipotent affine automorphisms Abstract: Let k be a field of characteristic zero, P = k[x_1,...,x_n] be a polynomial algebra, and J be the n x n lower triangular Jordan block. Let f = J and g = J - e_1, where e_1 = (1,0,...0)^t. Then f and g are automorphisms of P. It is well-known that the algebra of invariants of P under the action of g (call it G) is a polynomial algebra in n-1 variables. We will show that G has explicit generators of degree two and three. Then we will use these explicit generators of G to find an explicit vector space basis for the quadratic invariants in F and a transcendence basis for F. This talk will follow the paper by V. Bavula and T. Lenagan "Quadratic and cubic invariants of unipotent affine automorphisms".

Thursday, September 23 Geometry and Topology Seminar Time: 3:00-4:00pm Location: Eads, Room 116

Speaker: Professor Renato Feres Department of Mathematics, Washington University in St. Louis

Host: Prof. Xiang Tang Title: Billiards, Markov chains, and statistical mechanics Saturday, September 25 Conference

Time: 10:30am-4:30pm Location: Cupples I, Room 199 Hosts: Profs. Sophia Hayes and John McCarthy

Title: Frontiers in Technology and Science conference Speakers: Mark Alford, PhD, professor of physics in Arts & Sciences; Mihail Berezin, PhD, assistant professor of radiology in the School of Medicine; Liviu Mirica, PhD, assistant professor of chemistry in Arts & Sciences; Simine Vazire, PhD, assistant professor of psychology in Arts & Sciences; Paul Schlesinger, MD, PhD, associate professor of cell biology and physiology in the School of Medicine; and Kilian Weinberger, PhD, assistant professor of computer science and engineering in the School of Engineering and Applied Science, Washington University in St. Louis


Speaker: Kabe Moen Department of Mathematics, Washington University in St.Louis Title: Recent progress in weighted inequalities for singular integrals Abstract: We will talk about some very recent results in weighted theory for singular integrals. Topics include: the solution of the so called `A_2 conjecture', a counterexample for the Muckenhoupt Wheeden conjecture, and some progress on the two weight inequalities for the Hilbert transform. We also present a joint work with D. Cruz-Uribe on sufficient conditions for two weight inequalities of commutators of singular integrals.

Monday, September 27 Graduate Seminar Time: 5:00-6:00pm Location: Cupples I, Room 199 Host: Prof. Ed Spitznagel

Speaker: Professor Quo-Shin Chi Department of Mathematics, Washington University in St.Louis Title: A promenade through the history of the classification of isoparametric hypersurfaces Abstract: Isoparametric surfaces in the Euclidean 3-space, defined by two PDEs, arose in the study of geometric optics in 1918; the notion of an isoparametric hypersurface can thus be defined on any Riemannian manifold. The classification of isoparametric hypersurfaces in the Euclidean n-space started in 1937 by T. Levi-Civita, to be followed by the beautiful investigations of E. Cartan into the hyperbolic and the spherical cases. The spherical case turns out to be remarkably deep. As the ensuing study since 1940 to this date has witnessed, the spherical case is at the cross road of several important fields of mathematics, such as representation theory of Lie groups, symmetric spaces, algebraic topology, homotopy theory, etc., let alone differential geometry. I will bring another field of mathematics, namely, commutative algebra and algebraic geometry, to the cross road that turns out to play a decisive role for the classification problem, which has almost been completed barring three remaining cases. The talk will be non-technical, through which I intend to introduce glimpses of how important fields of mathematics interplay with the beautiful isoparametric geometry.

Tuesday, September 28 Math Club Time: 5:30-6:30pm Location: Cupples I, Room 199 Host: Prof. John McCarthy

Speaker: Professor John Shareshian Math Club Schedule

Wednesday, September 29 Algebraic Geometry Seminar Time: 4:00-5:30pm Location: Cupples I, Room 207 Host: Prof. Mohan Kumar

Speaker: Professor G.V. Ravindra Department of Mathematics, University of Missouri, St.Louis Title: The Picard-Lefschetz formula and a conjecture of Kato: the case of Lefschetz fibrations (Cont.)


Speaker: Professor Xiang Tang Department of Mathematics, Washington University in St. Louis Title: Atiyah class and Todd class Abstract:The Todd class in the Hirzebruch Riemann-Roch theorem looks so close to the Jacobian of the exponential map of a Lie group. I will report some recent works by Kapranov-Markarian-Ramadoss on Atiyah class explaining this similarity. If time is available, I will discuss a program to understand the Riemann-Roch theorem for orbifolds.

October 2010 - Talks Contact Marie Taris for details.

Friday, October 1 Wavelet Seminar Time: 3:30-4:30pm Location: Cupples I, Room 199 Host: Prof. Guido Weiss

Speaker: Professor Edward Wilson Department of Mathematics, Washington University in St.Louis Title: An exotic sampling function

Monday, October 4 Analysis Seminar Time: 4:00-5:00pm Location: Cupples I, Room 199 Host: Prof. John McCarthy

Speaker: Professor John McCarthy Department of Mathematics, Washington University in St.Louis Title: Matrix monotone functions of several variable

Monday, October 4 Graduate Seminar Time: 5:00-6:00pm Location: Cupples I, Room 199 Host: Prof. Ed Spitznagel

Speaker: Professor M. Victor Wickerhauser Department of Mathematics, Washington University in St.Louis Title: Two Simple Nonlinear Edge Detectors Abstract:Using moments of the local Fourier transform of a function one can build nonlinear filters that distinguish singularities. These may be used to find edges in digital images. The two simplest cases are described in closed form, and an algorithm for the general case is presented.

Wednesday, October 6 Algebraic Geometry Seminar Time: 4:00-5:30pm Location: Cupples I, Room 207 Host: Prof. Mohan Kumar

Speaker: Professor Matt Kerr Department of Mathematics, Washington University in St. Louis Title: Limits of Abel-Jacobi maps Abstract:We explain how motivic cohomology of singlar varieties can be constructed, and how to use it to compute limits of normal functions of geometric origin. The talk will also cover how this fits in with the Clemens-Schmid sequence, limits of admissible VMHS, and (sometimes) higher cycles on the total space.

Wednesday, October 6 Combinatorics Seminar Time: 4:00-5:00pm Location: Cupples I, Room 199 Host: Russ Woodroofe

Speaker: Professor Cindy Traub Department of Mathematics, Southern Illinois University, Edwardsville Title: Unfolding Orthogonal Polyhedra Abstract: A classic question of polyhedral unfolding concerns whether or not the surface of a given polyhedron can be unfolded into the plane without its faces overlapping. I will present the techniques of Biedl, Demaine, et.al., for unfolding two special classes of polyhedra: orthostacks and orthotubes. I will also give an overview of what is known and what problems remain open in this area.

Thursday, October 7 Geometry and Topology Seminar Time: 3:00-4:00pm Location: Eads, Room 116 Host: Prof. Xiang Tang

Speaker: Liwei Chen Department of Mathematics, Washington University in St. Louis Title: Ricci Flow Abstract: Historically, the Ricci flow technique was introduced by R. Hamilton, who wanted to use it to prove the Poincare's conjecture. Following Hamilton's work, Perelman eventually solved the conjecture. Recently, S. Brendle and R. Shoen proved the differential sphere theorem by using the Ricci flow technique. The Ricci flow is a very powerful tool in differential geometry. In this talk, we will focus on Hamilton's 1982 result: 3-manifold with positive Ricci curvature, in which the Ricci flow was first introduced. At the end of the talk, we will spend some time discussing the differential sphere theorem, in order to make a connection to the Roever Lecture that S. Brendle gave last semester.

Monday, October 11 Lecture Time: 12:00-1:00pm Location: Cupples I, Room 199 Host: Prof. Mohan Kumar

Speaker: Dr. Adam Ginensky WH Trading Title: An informal introduction to Mathematics in Finance Abstract:This will be an informal talk with somewhere between very little and no 'real mathematics'. We will discuss two things: 1)some of the things a quant should know and 2) some of the things a quant is expected to do. The idea is to give a person with a good background in mathematics (e.g. a math major) some ideas about what is needed to transition into a career in finance. The talk will be based on

the lecturer's personal experience, and hence will be very idiosyncratic and not at all encyclopedic.


Speaker: Professor Nan Lin Department of Mathematics, Washington University in St.Louis Title: Statistical Analysis of Next-Generation Sequencing Data Abstract: In the past few years, development in next-generation sequencing (NGS) technologies has revolutionized genomics because of the capability of sequencing DNA at unprecedented speed. As their effects are becoming increasingly widespread, there is a great demand in developing analysis tools for NGS data. In this talk, I will provide an introduction to the NGS data and discuss the statistical challenges.

Tuesday, October 12 Math Club Time: 5:30-6:30pm Location: Cupples I, Room 199 Hosts: Prof. John McCarthy & Shubho Sadhu

Speaker: Professor Matt Kerr Title: So you want to play elliptic billiards. Abstract:Then first you'll have to construct the table, which game regulations insist must pass through 5 given points. When you're done with that I'll pick N<10, and to beat me you have to shoot the ball (from wherever I put it) so it returns in exactly N steps to where it started. If you're not put off by a vector space of polynomials, you can make the elliptic table; and if you know how to spot a complex torus, then (with practice and foci) you can win. This is how I trap unsuspecting students into learning a bit of algebraic geometry.


Speaker: Professor Adrian Clingher Department of Mathematics, University of Missouri, St. Louis Title: Type II Degenerations of K3 Surfaces: A Survey of Classical Results


Speaker: Professor John Shareshian Department of Mathematics, Washington University in St. Louis Title: The work of Benedetti and Ziegler on LC-manifolds


Speaker: Tejas Kalelkar Department of Mathematics, Washington University in St. Louis Title: Heegaard splittings of 3-manifolds Abstract: Every closed 3-manifold $M$ contains a surface $S$ inside it such that cutting $M$ along $S$ gives us two pieces, both of which are handlebodies. In general, there may be infinitely many such (non-isotopic) surfaces $S$ inside $M$. Tao Li has shown that when a manifold does not contain any $pi_1$-injective surface, then there are in fact only finitely many such surfaces $S$ (up to isotopy). I will give an outline of his proof, some examples and end with a conjecture for extending this result (with modifications) to manifolds that may contain $\pi_1$-injective surfaces.

Thursday, October 14 Colloquium Time: Tea: 3:45pm Talk: 4:15-5:15pm Location: Cupples I, Room 199 Host: Prof. Nan Lin

Speaker: Professor Douglas Simpon Department of Statistics, University of Illinois at Urbana-Champaign Title: Statistical Methods for Biomedical Research on Diagnostic Ultrasound Abstract: Diagnostic ultrasound is among the most widely used imaging techniques in biomedicine. Common uses include prenatal ultrasonic imaging of the fetus, echocardiogram images of the heart and, increasingly, ultrasound imaging of the breast as an adjunct to x-ray mammography or as an aid to biopsy. Current research in this area aims to extend the range of applications and increase the power of ultrasonic imaging through techniques such as high frequency/ high acoustic pressure imaging, quantitative ultrasound analysis, and 3D impedance mapping. Some statistical issues and results associated with these efforts will be presented including analysis of semi-continuous response data in safety studies, image segmentation, pattern recognition, and tissue characterization.

Monday, October 18 Analysis Seminar Time: 4:00-5:00pm Location: Cupples I, Room 199 Host: Prof. Albert Baerstein

Speaker: Professor Bartlomiej Siudeja Department of Mathematics, University of Illinois at Champaign-Urbana Title: The method of rotations tight frames: sharp upper bounds on > Laplace eigenvalues Abstract: Extremal domains often possess rotational symmetry, for example, equilateral triangles, squares and disks, or in higher dimensions the regular simplexes, cubes and balls. We show how to exploit this symmetry to prove sharp upper bounds on sums of eigenvalues of the Laplacian. Notable features of the method are that it applies for all major boundary conditions

(Dirichlet, Robin or Neumann), for eigenvalue sums of arbitrary length, and that it requires no explicit knowledge of the eigenvalues or eigenfunctions of the extremal domain. [Joint work of R. S. Laugesen and B. A. Siudeja.]


Speaker: Professor Mohan Kumar Department of Mathematics, Washington University in St.Louis Title: Matrices over Polynomial Rings Abstract: I will discuss various results on matrices over Polynomial Rings. I will try to keep the talk as elementary as possible, but may quote deep results from algebraic geometry as and when needed. This topic has permeated my work in some form or the other for several decades and I hope you would find it as fascinating as I do.


Speaker: Professor Matt Kerr Department of Mathematics, Washington University in St. Louis Title: Limits of Abel-Jacobi maps (Continued) Abstract:We explain how motivic cohomology of singlar varieties can be constructed, and how to use it to compute limits of normal functions of geometric origin. We will start by reviewing higher Chow groups and regulator/AJ maps, giving a few more examples. The program will then be: (a) AJ on singular varieties, (b) limits of AJ maps (e.g. normal functions), (c) a splitting of the MHS of the central (singular) fibre and its effect on (b).


Speaker: Prof. Gary Jensen Department of Mathematics, Washington University in St. Louis Title: A global result for the Bonnet problem Abstract: Bonnet's problem is to find connected immersed surfaces in Euclidean space that admit another non-congruent immersion with the same first fundamental form and the same mean curvature. Such a deformation is called a Bonnet mate of the given immersion. If an immersion has at least two non-congruent mates, and the mean curvature is non-constant, then it is called properly Bonnet. We prove that if a surface M has a proper Bonnet immersion, then there exists a non-constant holomorphic function w = u+iv of M into the Poincare' right half space that satisfies the differential equation dw = -u rho, where rho is a 1-form on M determined by the derivative of the mean curvature. Results of Bonnet, Lawson-Tribuzy, and Chern follow as simple corollaries. This is joint work with Emilio Musso.

Thursday, October 21 Colloquium Time: Tea: 3:45pm Talk: 4:15-5:15pm Location: Cupples I, Room 199 Host: Prof. Alvaro Pelayo

Speaker: Professor Tudor Ratiu Endowed Chair Professor of Geometric Analysis and Director, Bernoulli Center of Mathematics Title: TBA Abstract: TBA

Monday, October 25 Analysis Seminar Time: 4:00-5:00pm Location: Cupples I, Room 199 Host: Prof. Richard Rochberg

Speaker: Professor Richard Rochberg Department of Mathematics, Washington University in St.Louis Title: Distances From a Reproducing Kernel Hilbert Space Abstract: You can use a reproducing kernel Hilbert space of functions on X to generate distance functions on X. I will discuss several ways to do this, how the functions are related to each other, where they arise, and some of their properties.


Speaker: Professor Matt Kerr Department of Mathematics, Washington University in St.Louis Title: Catalan's constant, a family of elliptic curves, and ??????? Abstract: We'll see how algebraic geometry over the complex numbers can shed light on a number-theoretic identity ascribed to Ramanujan, which links a hypergeometric function with a famous constant. In the process of doing this, we'll be led to introduce the mysterious object ??????? in the title. Though the talk will focus on one example, this more abstract construction produces many more such identities -- which, it so happens, compute constants of importance in string theory.

Tuesday, October 26 Math Club Time: 5:30-6:30pm Location: Cupples I, Room 199 Hosts: Prof. John McCarthy & Shubho Sadhu

Speaker: Professor Steven Krantz Title: A matter of gravity Abstract: We discuss some new perspectives on the concept of center of gravity. Matters of stability are treated. Asymptotic results in higher dimensions are

discussed. Required background is minimal. Wednesday, October 27 Algebraic Geometry Seminar

Time: 4:00-5:30pm Location: Cupples I, Room 207 Host: Prof. Mohan Kumar

Speaker: Professor Adrian Clingher Department of Mathematics, University of Missouri, St. Louis Title: Type II Degenerations of K3 Surfaces: A Survey of Classical Results (Continued)


Speaker: Professor Cindy Traub Department of Mathematics, Southern Illinois University, Edwardsville Title: Classifying Polyhedral Geodesics: Convex Deltahedra Abstract: We present a complete classification of all simple closed geodesics on the eight convex deltahedra. These results are joint work with Kyle Lawson, Jim Parish, and Adam Weyhaupt. This extends the recent classification by Fuchs and Fuchs of all simple closed geodesics on the five regular polyhedra.


Speaker: Prof. Larry Conlon Department of Mathematics, Washington University in St. Louis Title: Classification of finite depth foliations with a given substructure Abstract: Taut, smooth (respectively, topological) finite depth foliations of 3-manifolds have played important roles in knot theory. The substructure S of such a foliation is the union of leaves with nontrivial holonomy, a closed and nowhere dense set. The restriction of the foliation to each component U of the complement of S is a fibration over a 1-manifold. The classification envisioned (and largely proven) identifies all possible fibrations of each U that complete the substructure to a smooth (respectively, topological) foliation. These fibrations are determined, up to isotopy, by the rational rays in the interiors of finitely many nonoverlapping polyhedral cones in a certain cohomology space associated to U.

Thursday, October 28 Loeb Lecture Time: Tea: 3:45pm Talk: 4:15-5:15pm Location: Cupples I, Room 199 Host: Prof. John Shareshian

Speaker: Professor Richard Stanley Department of Mathematics, Massachusetts Institute of Technology Title: A survey of alternating permutations Abstract: An *alternating permutation* w = a_1 ... a_n of 1,2,...,n is a permutation such that a_i>a_{i+1} if and only if i is odd. If E_n (called an *Euler number*) denotes the number of alternating permutations of 1,2,...,n, then \sum_n E_n x^n/n! = sec x + tan x. We will discuss such topics as other occurrences of Euler numbers in mathematics, umbral enumeration of classes of alternating permutations, and longest alternating subsequences of permutations.

November 2010 Contact Marie Taris for details.

Monday, November 1 Analysis Seminar: Major Oral Time: 4:00-5:00pm Location: Cupples I, Room 199 Host: Prof. John McCarthy

Speaker: Matthew Wallace Department of Mathematics, Washington University in St.Louis Title: J.M. Luttinger's rearrangement inequality for traces of heat kernels of domains in Rn Abstract: Click here.

Monday, November 1 Graduate Seminar Time: 5:00-6:00pm Speaker: Professor Xiang Tang

Location: Cupples I, Room 199 Host: Prof. Ed Spitznagel

Department of Mathematics, Washington University in St.Louis Title: An introduction to Atiyah-Singer index theorem Abstract: I will give an elemetary introduction to the beautiful Atiyah-Singer index Theorem.

Wednesday, November 3 Minor Oral Time: 1:00-2:00pm Location: Mallinckrodt, Room 304 Host: Prof. Steve Krantz

Speaker: Liwei Chen Department of Mathematics, Washington University in St. Louis Title: 3-manifolds with positive Ricci curvature Abstract: In this talk, we will talk about R. Hamlton's paper in which Ricci flow was first introduced. First, I will give a brief introduction and some basic properties of Ricci flow. Secondly, we will mainly focus on the limit of the ratio between maximum and minimum of the scalar curvature, although the existence and the convergence of the Ricci flow are also very important. Finally, by controlling the ratio, we can get the desired result, and I will sketch some ideas of that.

Wednesday, November 3 Combinatorics Seminar Time: 4:00-5:00pm Location: Cupples I, Room 199 Host: Russ Woodroofe

Speaker: Scott Cook Department of Mathematics, Washington University in St. Louis Title: Billiard Models from Markov Chains Abstract: A particle moving in a long tube repeatedly interacts with the walls of the tube. If these walls are rough, scattering (non-billiard looking bounces) will occur. We consider the geometry of the microstructure of the walls to define a Markov chain on the space of trajectories of the particle and explore the long term evolution of the probability distribution on those trajectories.

Wednesday, November 3 Algebraic Geometry Seminar Time: 4:00-5:30pm Location: Cupples I, Room 207 Host: Prof. Mohan Kumar

Speaker: Matthew Kerr Department of Mathematics, Washington University in St. Louis Title: Classifying spaces of Hodge structures, Part I Abstract:This is the first talk in a series, and will be kept rather elementary. I'll start with a reworking of the definition of Hodge structures, and then define their "symmetry" (or Mumford-Tate) groups. The key idea for subsequent talks, and the content of the "Basic Property" of M-T groups, is that these pick out the "putative algebraic cycles" in all powers of the given variety. A simplification of Deligne's beautiful proof of this property will be presented in detail.

Thursday, November 4 Geometry and Topology Seminar Time: 3:00-4:00pm Location: Eads, Room 116 Host: Prof. Xiang Tang

Speaker: Prof. Rachel Roberts Department of Mathematics, Washington University in St. Louis Title: Open Book Decompositions of 3-Manifolds Abstract: I will define open book decompositions and survey the interplay between open books, foliations and contact structures in 3-manifolds.

Thursday, November 4 Colloquium Time: Tea: 3:45-4:10pm Talk: 4:10-5:10pm Location: Cupples I, Room 199 Host: Prof. Nan Lin

Speaker: Professor Jiashun Jin Department of Mathematics, Carnegie Mellon University Title: Higher Criticism Thresholding: Optimal Feature Selection when Useful Features are Rare and Weak Abstract: Click here.

Monday, November 8 Analysis Seminar Time: 4:00-5:00pm Location: Cupples I, Room 199 Host: Prof. John McCarthy

Speaker: Professor Virginia Naibo Department of Mathematics, Kansas State University Title: On bilinear pseudodifferential operators Abstract: Since the pioneering work of Coifman and Meyer in the 70's, the theory of bilinear pseudodifferential operators has largely evolved due to their applications in analysis and PDE's; in particular, to boundedness properties of commutators, bilinear singular integrals and paraproducts; and Liebniz rule-type inequalities. In this talk we will go over the theory of bilinear pseudo-differential operators and some of its applications, recent results and open problems.

Monday, November 8 Graduate Seminar Time: 5:00-6:00pm Location: Cupples I, Room 199 Host: Prof. Ed Spitznagel

Speaker: Professor Ed Wilson Department of Mathematics, Washington University in St.Louis Title: Exotic Idempotents on the Integers and Associated Exotic Sampling Functions Abstract: A function c on the additive group of integers is an idempotent if the group convolution of c with itself is defined and is equal to c. The easiest idempotent is the Dirac delta function at 0. Other relatively easy idempotents arise from passing to Fourier series; as long as the Fourier series m of c is defined, c is an idempotent when the periodic function m is equal to its pointwise square almost everywhere. Exotic idempotents are those which can't be obtained by Fourier series

methods. We'll discuss a large family of sparse (relatively few non-zero values) exotic idempotents obtained from a technique devised by Nik Weaver. We'll also show how each idempotent on the integers leads to a collection of sampling functions and give examples of exotic sampling functions arising from sparse exotic idempotents. It seems plausible that the sparse exotic idempotents should have non-trivial applications to combinatorics and to complex function theory but, since they were only invented two months ago, it's too early to be sure about this.

Tuesday, November 9 Math Club Time: 5:30-6:30pm Location: Cupples I, Room 199 Hosts: Prof. John McCarthy & Shubho Sadhu

Speaker: Professor Rachel Roberts Title: Seeing in high dimensions Abstract: I will define n-manifold, give *many* examples of n-manifolds, and describe a way of visualizing n-manifolds.

Wednesday, November 10 Algebraic Geometry Seminar Time: 4:00-5:30pm Location: Cupples I, Room 207 Host: Prof. Mohan Kumar

Speaker: Matthew Ballard Department of Mathematics, University of Pennsylvania Title: Orlov Spectra of Categories Arising in Mirror Symmetry Abstract:This is joint work with D. Favero and L. Katzarkov. A simple question to ask about an object G in a triangulated category T is the following: can every other object be built from G using cones, shifts, finite coproducts, and splitting of summands? If the answer is yes, then G is called a generator of T. If G is a generator, then a natural follow-up question is: how many cones do we have use? In particular, is there a uniform bound? The minimal upper bound is called the generation time of G. To T, we can associate a subset of the non-negative integers which records the generation times of all generators of T. It is called the Orlov spectrum of T. In this talk, we will take some categories of interest in mirror symmetry and discuss the structure of their Orlov spectra. Upper and lower bounds for the Orlov spectrum will be tied closely to geometry. Examples to be considered include: Calabi-Yau hypersurfaces in projective space, Riemann surfaces, and isolated hypersurface singularities.

Thursday, November 11 Colloquium Time: Tea: 3:45-4:10pm Talk: 4:10-5:10pm Location: Cupples I, Room 199 Host: Prof. Mohan Kumar

Speaker: Professor Kirti Joshi Department of Mathematics, University of Arizona Title: TBA Abstract: TBA


Speaker: Professor John McCarthy Department of Mathematics, Washington University in St.Louis Title: TBA

Thursday, November 18 Colloquium Time: Tea: 3:45-4:10pm Talk: 4:10-5:10pm Location: Cupples I, Room 199 Host: Prof. Rachel Roberts

Speaker: Professor John Baldwin Department of Mathematics, Princeton University Title: TBA Abstract: TBA


Speaker: Professor David Wright Department of Mathematics, Washington University in St.Louis Title: TBA


Speaker: Professor Renato Feres Department of Mathematics, Washington University in St.Louis Title: TBA Abstract: TBA

Tuesday, November 30 Math Club Time: 5:30-6:30pm Location: Cupples I, Room 199 Hosts: Prof. John McCarthy & Shubho Sadhu

Speaker: Professor Roya Beheshti Zavareh Title: The ABC conjecture Abstract: I will first discuss the "abc theorem" for polynomials which roughly says that if two polynomials with zeros of large multiplicity are added, their sum cannot have any zeros of large multiplicity. The proof of this result is short and simple. Then I will talk about a similar question which can be formulated for integers instead of polynomials. However, contrary to the case of polynomials, the question for integers turns out to be one of the most important unsolved problem in number theory: the so-called "abc conjecture".

December 2010 Contact Marie Taris for details.

Wednesday, December 1 Combinatorics Seminar Time: 4:00-5:00pm Location: Cupples I, Room 199 Host: Russ Woodroofe

Speaker: Russ Woodroofe Department of Mathematics, Washington University in St. Louis Title: Finding co-chordal covers of graphs Abstract: The co-chordal cover number of a graph G is the minimum number of subgraphs with chordal complement required to cover the edges of G. I'll show techniques for bounding and/or calculating the co-chordal cover number, relate the co-chordal cover number with other graph invariants, and discuss a connection with Castelnuovo-Mumford regularity of the associated edge ideal.

Thursday, December 2 Roever Lecture Time: Tea: 3:45-4:15pm Talk: 4:15-5:15pm Location: Cupples I, Room 199 Host: Prof. Alvaro Pelayo

Speaker: Professor Nicolai Reshetikhin Department of Mathematics, University of California, Berkeley Title: Understanding random surfaces Abstract: The talk will focus on random discrete surfaces which are closely related to tilings of a region in a plane and dimer models in statistical mechanics. In special cases they are also closely related to combinatorics of partitions. When the size of the region increases such surface converges in probability to a deterministic shape known as the limit shape. In some important special cases limit shapes can be described by algebraic curves. Fluctuations around limit shapes remain at the smaller scale. If time permit, I will describe key features of fluctuations and how such random discrete surfaces are related to random matrices.

Friday, December 3 Geometry and Topology Seminar Time: 2:00-3:00pm Location: Cupples I, Room 199 Host: Prof. Xiang Tang

Speaker: Professor Nicolai Reshetikhin Department of Mathematics, University of California, Berkeley Title: Hamiltonian Structures in Gauge Theory

Monday, December 6 Analysis Seminar Time: 4:00-5:00pm Location: Cupples I, Room 199 Host: Prof. John McCarthy

Speaker: Professor Xiang Tang Department of Mathematics, Washington University in St.Louis Title: Rankin-Cohen brackets, Hankle forms, and deformations

Tuesday, December 7 Math Club Time: 5:30-6:30pm Location: Cupples I, Room 199 Hosts: Prof. John McCarthy & Shubho Sadhu

Speaker: Andy Soffer Title: What the Greeks Couldn't Do Abstract: Back in the day the Greeks tried to construct some stuff without being able to measure exactly. They had straightedges and compasses, so they could draw circles and lines, but couldn't measure out distances or angles. Sometimes they were successful, but not always. We'll work through the four classical Greek problems that took well over a thousand years to be resolved. Hopefully we can work through them in under an hour.

Wednesday, December 8 Algebraic Geometry Seminar Time: 4:00-5:30pm Location: Cupples I, Room 207 Host: Prof. Mohan Kumar

Speaker: Professor Matthew Kerr Department of Mathematics, Washington University in St.Louis Title: Classifying spaces of Hodge structures, Part IV Abstract:In this last talk in the series, I will survey several aspects -- subdomains and CM points, Kato-Usui boundary components, and automorphic cohomology -- of Mumford-Tate domains. This will be done mainly through the running example of the ball model for the domain associated to U(2,1).

Thursday, December 9 Thesis Defense Time: 10:00-11:30am Location: Cupples I, Room 6 Host: Prof. Nan Lin

Speaker: Qing Li Department of Mathematics, Washington University in St. Louis Title: On Bayesian Regression Regularization Methods Abstract: Regression regularization methods, where penalty terms on model parameters are usually added to the standard loss functions, are recently drawing

increasing attention from researchers. Among others, elastic net is a flexible regularization and variable selection method that uses a mixture of L_1 and L_2 penalties. It is particularly useful when there are much more predictors than the sample size. The first part of this thesis proposes a Bayesian method to solve the elastic net model using a Gibbs sampler. While the marginal posterior mode of the regression coefficients is equivalent to estimates given by the non-Bayesian elastic net, the Bayesian elastic net has two major advantages. Firstly, as a Bayesian method, the distributional results on the estimates are straightforward, making the statistical inference easier. Secondly, it chooses the two penalty parameters simultaneously, avoiding the "double shrinkage problem" in the elastic net method. Real data examples and simulation studies show that the Bayesian elastic net behaves comparably in prediction accuracy but performs better in variable selection. The regularization methods also have been shown to be effective in quantile regressions in improving the prediction accuracy. The second part of this thesis studies regularization in quantile regressions from a Bayesian perspective. By proposing a hierarchical model framework, we give a generic treatment to a set of regularization approaches, including lasso, elastic net and group lasso penalties. Gibbs samplers are derived for all cases. This is the first work to discuss regularized quantile regression with the elastic net penalty and the group lasso penalty. Both simulated and real data examples show that Bayesian regularized quantile regression methods often outperform quantile regression without regularization and their non-Bayesian counterparts with regularization.

Thursday, December 9 Geometry and Topology Seminar Time: 3:00-4:00pm Location: Eads, Room 116 Host: Prof. Xiang Tang

Speaker: Prof. Quo-Shin Chi Department of Mathematics, Washington University in St. Louis Title: Taut submanifolds are algebraic Abstract: A compact submanifold in Euclidean space is taut if the nondegenerate (i.e., Morse) distance functions are perfect Morse functions. It turns out this is equivalent to that all the distance functions are perfect Morse-Bott functions. Kuiper raised the question in 1984 whether all taut submanifolds are real algebraic. In an earlier paper of Cecil, Chi and Jensen, we verified that, for dimension no greater than 4, every taut submanifold is a connected component of a real irreducible algebraic variety. In this talk I will sketch a proof that removes the dimension restriction. Since tautness is a conformal invariant, the proof is more conveniently carried out in the sphere. This question of Kupier is a beautiful interplay between differential geometry, real algebraic geometry and differential topology.

Monday, December 13 Analysis Seminar Time: 4:00-5:00pm Location: Cupples I, Room 199 Host: Prof. John McCarthy

Speaker: Professor Wing-Suet Li Department of Mathematics, Georgia Tech. Title: Intersection of subspaces and inequalities of the eigenvalues of sums of selfadjoint operators Abstract: We will discuss some of the basic ideas on the intersection of subspaces that will lead to inequalities of the eigenvalues of sums of selfadjoint operators.

Wednesday, December 22 Minor Oral Time: 3:00-4:00pm Location: Cupples I, Room 6 Host: Prof. David Wright

Speaker: Brady Brock Department of Mathematics, Washington University in St. Louis Title:The equivalence of the Jacobian conjecture and the vanishing conjecture Abstract:Let k be a field of characteristic zero. The Jacobian conjecture asserts that every polynomial map in n variables having unital Jacobian determinant is invertible. Recently, it has bee shown that the Jacobian conjecture is equivalent to the vanishing conjecture of quadratic differential operators with constant coefficients. In this talk I will present a special case of this equivalence. Namely, that the vanishing conjecture on 2n variables is equivalent to the Jacobian conjecture on n variables.

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