# 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

October 22, 2013 6:00 pm (Tuesday)

## Counting for Advanced Mathematicians

Brian Simanek, Vanderbilt University
Location: Stevenson 1206

Our mathematics education parallels the history of mathematics in that it all began with counting.  At a very young age, we understood the idea of quantity and - more importantly - how to compare quantities.  Then, somewhere along the way we vaguely became aware of this mysterious idea called infinity that somehow answered the question we all posed to our first grade teachers: "What is the largest number?"  The main point of this talk will be to demonstrate that infinity does not really answer this question because there are different sizes of infinity!  As strange as this may seem, we will try to understand how this can be the case and mention some different ways that mathematicians describe the size of a set when counting is not sufficient.

October 21, 2013 3:10 pm (Monday)

## Circumference and Pathwidth of Highly Connected Graphs

Emily Marshall, Vanderbilt University
Location: Stevenson 1432

Birmele proved that every graph with circumference t has treewidth at most t-1. Under the additional assumption of 2-connectivity, results of Nesetril and Ossona de Mendez show that such graphs have bounded pathwidth, which is a qualitatively stronger conclusion. We make a factor-2 improvement to their bound. Birmele's theorem was extended by Birmele, Bondy and Reed who showed that every graph without k disjoint cycles of length at least t has bounded treewidth (as a function of k and t). Our main result states that, under the additional assumption of (k + 1) connectivity, such graphs have bounded pathwidth. In fact, they have pathwidth O(t^3 + tk^2). Moreover, examples show that (k + 1)-connectivity is required for bounded pathwidth to hold. These results suggest the following general question: for which values of k and graphs H does every k-connected H-minor-free graph have bounded pathwidth? We discuss this question and provide a few observations. This is joint work with David Wood at Monash University.

October 21, 2013 3:00 pm (Monday)

## Unique Cartan Subalgebras and Solidity Results for II_1 factors

Chenxu Wen, Vanderbilt University
Location: Stevenson 1404

The recent development in the rigidity results in the study of II_1 factors from the group-measure-space construction has lead to many new insights to the structure of certain factors. Of particular importance in the theory is the unique Cartan subalgebra (or group-measure-space Cartan), up to unitary conjugacy, for some II_1 factors. In the talk we will discuss the work in this direction started by Ozawa and Popa and followed by many others. As the consequence of the techniques involved, we will also talk about some solidity results for some group von Neumann algebras.

October 18, 2013 4:10 pm (Friday)

## Reduction to Type II in Dynamical Systems

Kamran Reihani, Vanderbilt University
Location: Stevenson 1432

The talk reports on a frequently used strategy that seems to be useful when some sort of "type-III" phenomena prevent the existence of invariant structures for dynamical systems. The approach is called "reduction to type II" (in analogy with the reduction of type-III factors to type II in the theory of von Neumann algebras). It 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. We will discuss a few examples in geometry, topology, and measure theory. The reduction process in the measurable case naturally involves Tomita-Takesaki theory, and the computations are based on a joint work with Bill Paschke.

October 16, 2013 4:10 pm (Wednesday)

## Lattices in Amenable Groups

Tsachik Gelander, Hebrew University and Weizmann Institute
Location: Stevenson 1310

Let G be a locally compact amenable group. We discuss the question whether every closed subgroup of finite covolume in G is cocompact. Joint work with U. Bader, P.E. Caprace and S. Mozes.

October 16, 2013 3:30 pm (Wednesday)

## Graduate Student Tea

Location: Stevenson 1425

October 15, 2013 6:00 pm (Tuesday)

## The Brouwer Fix-Point Theorem

Yago Antolin Pichel, Vanderbilt University
Location: Stevenson 1206

Play Hex, Prove Brouwer

October 15, 2013 4:10 pm (Tuesday)

## Weakly Commensurable Groups

Andrei Rapinchuk, University of Virginia
Location: Stevenson 5211

The notion of weak commensurability (of Zariski-dense subgroups of semi-simple algebraic groups) was introduced in the ongoing joint work with Gopal Prasad on length-commensurable and isospectral locally symmetric spaces. We were able to determine when two arithmetic subgroups are weakly commensurable. This led to various geometric results, some of which are related to the famous question "Can one hear the shape of a drum?" Tea at 3:30 pm in SC 1425.

October 9, 2013 4:10 pm (Wednesday)

## "Stories from Another Pocket" (after Karel Capek and others).

Dmitry Burago, Penn State
Location: Stevenson 1310

This year, I have been delivering a number of talks under almost the same title. However, the talks are quite different. I have prepared about twenty topics, with two-three slides for each. For each talk, I select about eight topics; the choice depends on the audience, how long the talk is etc. The topics are united only by the fact they were of interest to me in the past several years. For each topic, I give only key definitions, one or two theorems and several open problems (which may form the most important part of the talk). The talk is supposed to be accessible to (reasonable) graduate students. We will not go into (almost:) any technicalities.

October 9, 2013 3:30 pm (Wednesday)

## Graduate Student Tea

Location: Stevenson 1425