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 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

October 9, 2013 3:10 pm (Wednesday)

An Introduction to Markov Chain Monte Carlo Methods

Jorge Roman, Vanderbilt University
Location: Stevenson 1307

The need to approximate an intractable integral with respect to a probability distribution P is a problem that frequently arises across many different disciplines. A popular alternative to numerical integration and analytical approximation methods is the Monte Carlo (MC) method which uses computer simulations to estimate the integral. In the MC method, one generates independent and identically distributed (iid) samples from P and then uses sample averages to estimate the integral. However, in many situations, P is a complex high-dimensional probability distribution and obtaining iid samples from it is either impossible or impractical. When this happens, one may still be able to use the increasingly popular Markov chain Monte Carlo (MCMC) method in which the iid draws are replaced by a Markov chain that has P as its stationary distribution. In this talk, I will give a brief introduction to the MC and MCMC methods. The focus will be on the MCMC method and its applications to Bayesian statistics.

October 8, 2013 6:00 pm (Tuesday)

Famous Proofs of the Pythagorean Theorem

Tim Ferguson, Vanderbilt University
Location: Stevenson 1206

You have probably heard of the Pythagorean theorem, but can you explain why it is true? I will explain several different proofs of this famous theorem, including proofs by Euclid and President Garfield.  If time permits, I will also discuss another famous result attributed to the Pythagoreans: the proof of the irrationality of the square root of 2.

October 7, 2013 4:05 pm (Monday)

Bach-Maxwell Equations and Extremal Kahler Metrics

Caner Koca, Vanderbilt University
Location: Stevenson 1312

The Bach-Maxwell Equations on a 4-dimensional compact oriented manifold can be thought of as a conformally invariant version of the classical Einstein-Maxwell Equations in general relativity. Riemannian metrics which solve the BM equations have interesting geometric properties. In this talk, I will introduce these equations and give several variational characterizations. I will also show that extremal Kahler metrics are among the solutions and discuss their role in this variational setting.

October 6, 2013 2:00 pm (Sunday)

Department Picnic

Location: Edwin Warner Park Area 11

October 4, 2013 4:10 pm (Friday)

The 3D Index of a Cusped Hyperbolic 3-Manifold

Stavros Garoufalidis, Georgia Tech
Location: Stevenson 1432

The 3D index of Dimofte-Gaiotto-Gukov is a partially defined function on the set of ideal triangulations of 3-manifolds with torus boundary, which is partially invariant under 2-3 moves. It turns out that an ideal triangulation has 3D index if and only if it is 1-efficient. Moreover, the 3D index descends to a topological invariant of cusped hyperbolic manifolds. Parts are joint work with Hodgson-Rubinstein-Segerman.

October 4, 2013 4:10 pm (Friday)

Analyticity of Solutions to the Yamabe Flow on Non-Compact Manifolds

Yuanzhen Shao, Vanderbilt University
Location: Stevenson 1307

The Yamabe flow can be considered as an alternative approach to the famous Yamabe problem. Nowadays there is increasing interest in studying the Yamabe flow on non-compact manifolds. We show by means of continuous maximal regularity theory and the implicit function theorem that in every conformal class containing at least one real analytic metric, solutions to the Yamabe flow immediately become analytic jointly in time and space. In comparison with the existing results, we do not ask for a uniform bound on the curvatures of the initial metric. We will also briefly discuss a generalization of our results on singular manifolds.

October 3, 2013 4:10 pm (Thursday)

The Stable Coefficients of the Jones Polynomial of a Link

Stavros Garoufalidis, Georgia Tech
Location: Stevenson 5211

The Jones polynomial of a link is a finite collection of integers placed at different degrees. We propose a structure theorem for the (stable) coefficients of an alternating link in terms of a flag algebra of graphs, verify it for the first 4 coefficients and present further experimental evidence for the next two. This leads to natural and open questions about categorification of alternating links, and to questions on the structure of flag algebras. Joint work with Thao Vuong and Sergey Norin. Tea at 3:30 pm in SC 1425.

October 2, 2013 4:10 pm (Wednesday)

Locally Compact Hyperbolic Groups

Dennis Dreesen, University of Southampton
Location: Stevenson 1310

The common convention when dealing with hyperbolic groups is that such groups are finitely generated and equipped with the word length metric relative to a finite symmetric generating subset. Gromov's original work on hyperbolicity already contained ideas that extend beyond the finitely generated setting. We study the class of locally compact hyperbolic groups and elaborate on the similarities and differences between the discrete and non-discrete setting.