Index This week Schedule & abstracts Past talks Organizer notes Graduate page

  Spring 2013 schedule
Date Speaker Title
28 August, 2013 Gleb Zhelezov Organizational Meeting
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04 September, 2013 Gleb Zhelezov Singularities and Coalescence in the Keller-Segel Model
Abstract: In its reduced form, the Keller-Segel chemotaxis model is a conservative system in which particle density is described by a convection–diffusion equation that's coupled to an elliptic equation for the evolution of the chemoattractant. For total mass above a certain threshold, the solution to this equation becomes singular in finite time, which causes most finite difference, spectral, and finite element methods to perform poorly. In this talk, we will introduce this system, investigate some of its analytic properties, and introduce a stochastic particle-in-cell method for its solution.
11 September, 2013 Dylan Murphy Algebraic curves and the KP equation
Abstract: The Kadomtsev-Petviashvili (KP) equation is an analogue of the famous Korteweg-de Vries (KdV) equation, which was the starting point for the modern theory of integrable systems. Several years after the development of the inverse scattering method for KdV, a different approach or constructing solutions was devised. This approach encodes the solution to the equation in the expansion coefficients of a special function on an algebraic curve. By using techniques from classical algebraic geometry, this function can be constructed explicitly and the corresponding solution calculated.

In this talk, I will discuss the application of this method to the KP equation and show some simple examples of the solutions that result.
18 September, 2013 Cody Gunton The Cohen-Lenstra Heuristics
Abstract: The ideal class group of a number field is an essential and very mysterious invariant. For even the simplest classes of number fields, little is known about the collection of all ideal class groups. The Cohen-Lenstra heuristics, first presented in 1983, successfully predict certain statistics of ideal class groups. This talk will introduce the basic players, conjectures and theorems the theory of ideal class groups, assuming no prior knowledge of algebraic number theory, and will discuss the Cohen-Lenstra heuristics and related results.
25 September, 2013 Erik Davis Wavelets
In this talk I will discuss wavelets & while you enjoy bagels.
02 October, 2013 Megan McCormick Jucys-Murphy elements and the center of the symmetric group ring
Abstract: Jucys-Murphy elements are specific sums of transpositions in the symmetric group ring, C[S_n]. These elements show up frequently in the representation theory of the symmetric group, and have some beautiful properties that lead to powerful results. I will go into some detail about how these elements are related to the center of the symmetric group ring and give a neat result (due to Jucys) about their eigenvalues. I will also discuss how they are helpful in a specific random matrix theory problem.
09 October, 2013 Rachel Baumann, Amy Been and Doron Shahar Topological Groups and Duality
Abstract: Topological groups represent objects in the intersection of the theory of groups and topological spaces. We can obtain some significantly stronger results about objects which are both groups and topological spaces. The goal of this talk will be to introduce topological groups and their Pontryagin duals, and explore what happens to nice topological properties upon dualizing.
16 October, 2013 Tova Brown The Loop Equations of Random Matrices
Abstract: The loop equations of random matrix theory have been used for quite some time to obtain explicit formulas for map enumeration generating functions. I want to use them to count certain families of graphs embedded on Riemann surfaces. But putting these loop equations on a rigorous mathematical foundation takes considerable work. Ercolani and McLaughlin did this in 2007. In this talk, I will be giving a broad overview of the steps in this derivation, as well as motivation for why we want to do it. Probability measures, random matrix theory, linear algebra, asymptotics, Riemann-Hilbert problems, contour integrations, and more will take their respective parts in this drama.

If you'd like to give a talk or find out more about the grad colloquium, please email Gleb Zhelezov , the colloquium organizer for Fall 2013.