# 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

April 8, 2013 4:10 pm (Monday)

## Topology of G_2 Manifolds

Mustafa Kalafat, Michigan State University
Location: Stevenson 1432

We analyze the topological invariants of some specific Grassmannians, the Lie group G_2, and give some applications. This is a joint work with Selman Akbulut.

April 8, 2013 3:30 pm (Monday)

## Group Planar Algebras

Corey Jones, Vanderbilt University
Location: Stevenson 1404

We will review the basic construction for group type subfactors, and describe the planar algebra of the standard invariant via generators and relations.  We will also discuss the annular modules of these planar algebras.

April 8, 2013 3:10 pm (Monday)

## Whitney-Tutte Polynomials of Ribbon Graph n-Cables

Phillip Jedlovec, Vanderbilt University
Location: Stevenson 1320

Given the ribbon graph D of a link diagram L, define D_n to be the ribbon graph of the n-cable of L. We study how D_n changes as n increases, and describe these ribbon graph changes in terms of graphical transformations. Given any ribbon graph D of a link diagram L, we use the transfer matrix technique given by Montee, Keller, and Stoltzfus, as well as contraction-deletion methods, to give a linear recursion on T(D_n; X, Y), with functions on X, Y, and n as coefficients, where T(D_n; X, Y) is the Whitney-Tutte polynomial of D_n.  This recursion relation makes it possible to calculate T(D_n; X, Y) in O(n^2) time. In addition, for ribbon graphs of alternating link diagrams we give a simpler linear recursion with which T(D_n; X, Y) can be calculated in O(n) time.
April 5, 2013 4:10 pm (Friday)

## On a Thermodynamically Consistent Stefan Problem with Variable Surface Energy

Gieri Simonett, Vanderbilt University
Location: Stevenson 1307

A thermodynamically consistent two-phase Stefan problem with temperature-dependent surface tension and with or without kinetic undercooling is studied. It is shown that this problem generates a local semiflow on a well-defined state manifold. Moreover, stability and instability results of equilibrium configurations will be presented. It will be pointed out that surface heat capacity has a striking effect on the stability behavior of multiple equilibria. (Joint work with J. Prüss and M. Wilke).

April 5, 2013 4:10 pm (Friday)

## Stabilizers of Actions of Product Groups and Lattices in Product Groups

Darren Creutz, Vanderbilt University
Location: Stevenson 1432

I will present my recent work on the stabilizers of actions of products of groups and irreducible lattices in products. The main results are a classification of all possible stabilizer groups for actions of products of Howe-Moore groups, at least one of which has (T), and a classification statement for actions of lattices in such products. In contrast to previous work (joint with J. Peterson) on stabilizers, the approach taken here does not involve writing lattices as commensurators and therefore applies even in the case when neither of the ambient groups are totally disconnected and in this sense complement the previous work.

April 3, 2013 4:10 pm (Wednesday)

## Small Cancellation in Aclyindrically Hyperbolic Groups

Micheal Hull, Vanderbilt University
Location: Stevenson 1310

In a recent seminar, Osin introduced the class of aclyindrically hyperbolic groups and showed this class coincided with several previously studied and seemingly distinct classes of groups. In this talk, we will present a version of small cancellation theory for aclyindrically hyperbolic groups. We will discuss the main tools of this theory and some applications of these tools, especially the construction of various exotic quotient groups.

April 3, 2013 3:30 pm (Wednesday)

## Embedding Theorem for Graph Planar Algebras

Yunxiang Ren, Vanderbilt University
Location: Stevenson 1227

In this talk we shall prove that every subfactor planar algebra embeds in the Graph planar algebra of its pricipal graph, and its generalization (as done by Scott Morrison and Kevin Walker). This talk will start from basic definitions, and will be accessible to anyone interested in subfactors or planar algebras.

April 3, 2013 3:10 pm (Wednesday)

## Fourier Bases on Fractals

Keri Kornelson, University of Oklahoma
Location: Stevenson 1307

The study of Bernoulli convolution measures dates back to the 1930's, yet there has been a recent resurgence in the theory prompted by the connection between convolution measures and iterated function systems (IFSs). The measures are supported on fractal Cantor subsets of the real line, and exhibit their own sort of self-similarity. We will use the IFS connection to discover Fourier bases on the L^2 Hilbert spaces with respect to Bernoulli convolution measures. There are some interesting phenomena that arise in this setting. We find that some Cantor sets support Fourier bases while others do not. In cases where a Fourier basis does exist, we can sometimes scale or shift the Fourier frequencies by an integer to obtain another ONB. We also discover properties of the unitary operator mapping between two such bases. The self-similarity of the measure and the support space can, in some cases, carry over into a self-similarity of the operator.

April 3, 2013 1:30 pm (Wednesday)