# Math Calendar

 Categories: Choose a category... View all categories _______________________ Biomath Seminar Colloquium Computational Analysis Seminar Departmental Student Awards Faculty Meeting Graph Theory and Combinatorics Seminar Informal von Neumann Algebras Seminar Noncommutative Geometry and Operator Algebras Seminar Partial Differential Equations Seminar Subfactor Seminar Symplectic and Differential Geometry Seminar Topology and Group Theory Seminar Undergraduate Seminar Universal Algebra and Logic Seminar Vandy Math Club RSS

###### » Seminar Pages

November 1, 2013 4:10 pm (Friday)

## Analyticity of Local Solutions to a Logarithmic Diffusion Equation

Naian Liao, Vanderbilt University
Location: Stevenson 1307

In this talk, I will explain some recent progress on the local behavior of a logarithmic diffusion equation. First of all, in spite of the singularity of the equation local solutions are analytic in space variable and arbitrarily differentiable in time variable if some appropriate conditions are satisfied. Secondly, a Harnack inequality in the topology of $L^1$ will be reported.

November 5, 2013 6:00 pm (Tuesday)

## Early and Often: How Voting Systems Affect Democracy and Math Affects Voting Systems

Matthew Smedberg, Vanderbilt University
Location: Stevenson 1206

To most Americans, voting is an infrequent, simple civic activity: you learn a little about the candidates, choose the one you like the most (or dislike the least!), mark a paper or electronic ballot, and move on with your life. Few of us reflect on how the electoral system might shape our public institutions, and still fewer on how the electoral system might be different, and how such changes could affect the power and workings of public institutions. We will discuss a few such ideas during this talk, including why the U.S. has a two-party system while other nations have several parties, and Arrow's Theorem stating (informally) that there is no perfect electoral system.

November 6, 2013 3:10 pm (Wednesday)

## Asymptotic Behavior of Positive Harmonic Functions in Certain Unbounded Domains

Koushik Ramachandran, Purdue University
Location: Stevenson 1307

We derive asymptotic estimates at infinity for positive harmonic functions in large class of non-smooth unbounded domains. These include domains whose sections, after rescaling, resemble a Lipschitz cylinder or a Lipschitz cone. Examples of such domains are various paraboloids and, horn domains.

November 6, 2013 3:30 pm (Wednesday)

Location: Stevenson 1425

November 7, 2013 4:10 pm (Thursday)

## Towards TDA

Shmuel Weinberger, University of Chicago
Location: Stevenson 5211

Topological data analysis is the idea that high dimensional large data sets can sometimes be more effectively understood by looking for an underlying geometric structure which can then be exploited for the purposes of analysis. (It is one of the themes of this year's special year at IMA.) In this talk I will try to explain some interesting problems that arise from this perspective: some good news and some bad news and then some more good news. Tea at 3:30 pm in SC 1425.

November 8, 2013 4:10 pm (Friday)

## Looking for Matrix Valued Tau Functions

Alberto Grünbaum, UC Berkeley
Location: Stevenson 1432

November 8, 2013 4:10 pm (Friday)

## Two-Phase Flows with Phase Transitions

Gieri Simonett, Vanderbilt University
Location: Stevenson 1307

A thermodynamically consistent model for two-phase flows including phase transitions driven by temperature is introduced and analyzed.

November 11, 2013 4:10 pm (Monday)

## Combinatorics and Complexity of Kronecker Coefficients

Greta Panova, UCLA
Location: Stevenson 4327

Kronecker coefficients lie at the intersection of representation theory, algebraic combinatorics and, most recently, complexity theory. They count the multiplicities of irreducible representations in the tensor product of two other irreducible representations of the symmetric group. While their study was initiated almost 75 years ago, remarkably little is known about them. One of the major problems of algebraic combinatorics is to find an explicit positive combinatorial formula for these coefficients. Recently, this problem found a new meaning in the field of Geometric Complexity Theory, initiated by Mulmuley and Sohoni, where certain conjectures on the complexity of computing and deciding positivity of Kronecker coefficients are part of a program to prove the "P vs NP" problem. In this talk we will give an overview of this topic and we will describe several problems with some results on different aspects of the Kronecker coefficients. We will explore Saxl conjecture stating that the tensor square of certain irreducible representation of S_n contains every irreducible representation, and present a criterion for determining when a Kronecker coefficient is nonzero. In a more combinatorial direction, we will show how to prove certain unimodality results using Kronecker coefficients, including the classical Sylvester's theorem on the unimodality of q-binomial coefficients (as polynomials in q). We will also present some results on complexity in light of Mulmuley's conjectures. The presented results are based on joint work with Igor Pak and Ernesto Vallejo. Tea at 3:30 pm in SC 1425.

November 12, 2013 4:10 pm (Tuesday)

## Effective Symmetry Breaking

Rebecca Steiner, Vanderbilt University
Location: Stevenson 1310

Symmetry breaking in combinatorics involves coloring the elements of a structure so that there are no nontrivial automorphisms of the structure which respect the coloring. We say that such a coloring distinguishes the structure. We apply computability theory to this notion and show that there is a computable, finite-valence, pointed graph which is distinguished by a 2-coloring but not by any computable 2-coloring. We also show that if a computable, finite-branching tree has a distinguishing 2-coloring, then it must have a 0''-computable distinguishing 2-coloring.

November 12, 2013 6:00 pm (Tuesday)

## Talk Title TBA

Corey Jones, Vanderbilt University
Location: Stevenson 1206

November 13, 2013 3:30 pm (Wednesday)

Location: Stevenson 1425

November 13, 2013 4:10 pm (Wednesday)

## Conjugacy Languages and Growth Series in Groups

Laura Ciobanu, University of Neuchatel
Location: Stevenson 1310

In this talk I will introduce two languages related to conjugacy in groups, and discuss their regularity in lots of classes of groups, including hyperbolic, virtually abelian, Artin and more. I will also present results regarding the conjugacy growth series in free products and graph products, and show that the conjugacy growth series of a virtually cyclic group is rational for all generating sets. This is joint work with Susan Hermiller, Derek Holt, and Sarah Rees.

November 14, 2013 4:10 pm (Thursday)

## Seeing Geometry in Certain Kinds of Modules

Ross Geoghegan, Binghamton
Location: Stevenson 5211

I'll begin by explaining a very primitive notion of non-positive curved space called a CAT(0) space. It's so simple that it can be understood by anyone who knows what a metric space is and who likes geometry. My CAT(0) space M will come with a group G of isometries of M. This leads to the notion of the limit set of this action of G. Much more interesting, and the focus of my talk, is a set of special limit points called the "horospherical limit set". After a short discussion of what this means in general I'll explain how it shows up in several parts of real mathematics: Fuchsian and Kleinian groups, discrete subgroups of Lie groups, and tropical geometry, as well as, more generally, the issue of trying to see geometry in the structure of ZG-modules. This is a colloquium talk arranged around my joint work with Robert Bieri. Tea at 3:30 pm in SC 1425.

November 15, 2013 (Friday)

## Computable Algebra: A Personal Perspective

I will survey some of my recent results about computable Artinian rings and Euclidean domains, while relating these results to classical (i.e. noncomputable) ring theory. In particular I will show that annihilator ideals play a central role in the theory of Artinian rings, and then construct transfinite Euclidean domains of all cardinalities, answering a question of P. Samuel, Nagata, and others.

November 15, 2013 4:10 pm (Friday)

## Uniqueness Questions for the Navier-Stokes Equation in the Hyperbolic Setting

Magdalena Czubak, Binghamton University (SUNY)
Location: Stevenson 1307

The smoothness and uniqueness of the Leray-Hopf solutions to the Navier-Stokes equation is well-known in 2D. Contrary to what is known in the Euclidean setting, in our previous work we showed that there is non-uniqueness in 2D for simply connected, complete manifolds with negative sectional curvature. The goal of this talk is to show how we can restore uniqueness. In the process, we develop the theory of weak solutions to the Navier-Stokes equations on the 2D hyperbolic space.  This is joint work with Chi Hin Chan.

November 18, 2013 4:10 pm (Monday)

## In Search of Invariant Structures in Analysis, Topology and Geometry

Kamran Reihani, Vanderbilt University
Location: Stevenson 1312

The talk reports on a frequent appearance of a strategy that seems to be useful when some sort of "type-III" phenomena prevent the existence of certain invariant structures for dynamical systems in analysis, topology and geometry. The approach is called "reduction to type II", and usually involves some extension of the dynamical system in such a natural way that the resulting system is large enough to carry the desired invariant structure. Our examples will demonstrate that - in search for such extensions - one naturally needs to involve (or to develop) some very important techniques relevant to the context.

November 19, 2013 4:10 pm (Tuesday)

## Computable Algebra: A Personal Perspective

Chris Conidis, Vanderbilt University
Location: Stevenson 1310

I will survey some of my recent results about computable Artinian rings and Euclidean domains, while relating these results to classical (i.e. noncomputable) ring theory. In particular I will show that annihilator ideals play a central role in the theory of Artinian rings, and then construct transfinite Euclidean domains of all cardinalities, answering a question of P. Samuel, Nagata, and others.

November 19, 2013 6:00 pm (Tuesday)

## Talk Title TBA

Zach Gaslowitz, Vanderbilt University
Location: Stevenson 1206

November 20, 2013 3:10 pm (Wednesday)

## Riesz Decomposition for the Farthest Distance Functions via Logarithmic, Green and Riesz Potentials

Igor Pritsker, Oklahoma State University
Location: Stevenson 1307

We discuss several versions of the Riesz Decomposition Theorem for superharmonic functions. This theorem is usually stated for Newtonian and logarithmic potentials in the literature, but it is also true for some Riesz kernels. However, no full version for Riesz potentials is available. We mention related topics on $\alpha$-superharmonic and polyharmonic functions, and on fractional Laplacian. We apply Riesz decompositions to obtain integral representations of the farthest distance functions for compact sets as logarithmic, Green and Riesz potentials of positive measures with unbounded support. The representing measures encode many geometric properties of compact sets via their distance functions.

November 20, 2013 3:30 pm (Wednesday)

Location: Stevenson 1425

November 20, 2013 4:10 pm (Wednesday)

## Counting Real Curves on K3 Surfaces

Rares Rasdeaconu, Vanderbilt University
Location: Stevenson 1310

Real enumerative invariants of real algebraic manifolds are derived from counting real curves with suitable signs. I will discuss the case of counting real rational curves on simply connected complex projective surfaces with zero first Chern class (K3 surfaces) equipped with an anti-holomorphic involution. An adaptation to the real setting of a formula due to Yau and Zaslow will be presented. The proof passes through results of independent interest: a new insight into the signed counting, and a formula computing the Euler characteristic of the real Hilbert scheme of points on a K3 surface, the real version of a result due to Gottsche. The talk is based on a joint work with V. Kharlamov.

November 21, 2013 4:10 pm (Thursday)

## Pushing Polynomial Reproducing Kernels to Their Nonpolynomial Limits

Doron Lubinsky, Georgia Tech
Location: Stevenson 5211

Polynomial reproducing kernels are an essential tool in analyzing orthogonal polynomials and orthogonal expansions. They also play a key role in universality limits for random matrices. We discuss these connections. Moreover, we analyze how such the limiting form of these polynomial kernels becomes the sinc kernel for Paley-Wiener spaces.