Fall 2009 Colloquium Schedule

Week
1 Wed., 9/9 x
2 Wed., 9/16 x
3 Wed., 9/23 x
4 Wed., 9/30 x
5 Wed., 10/7 x
6 Wed., 10/14 Henry Cohn, 4--5 pm in B&H 190.
7 Wed., 10/21 x
8 Wed., 10/28 Percy Deift, 4--5 pm in B&H 190.
9 Wed., 11/4 Sergey Fomin, 4--5 pm in B&H 190.
10 Wed., 11/11 Irina Mitrea, 4--5 pm in B&H 190.
11 Wed., 11/18 Juan Souto, 4--5 pm in B&H 190.
12 Wed., 11/25 x (Thanksgiving break)
13 Wed., 12/2

Spring 2010 Colloquium Schedule

Week
1 Wed., 1/27
2 Wed., 2/3
3 Wed., 2/10
4 Wed., 2/17
5 Wed., 2/24
6 Wed., 3/3
7 Thurs., 3/11 Andrea Bertozzi, Distinguished Lecture Series.
7 Fri., 3/12 Andrea Bertozzi, Distinguished Lecture Series.
8 Wed., 3/17
9 Wed., 3/24
Wed., 3/31 spring break, no colloquium
10 Wed., 4/7
11 Wed., 4/14
12 Wed., 4/21
13 Wed., 4/28
13 Wed., 5/5

Abstracts

Henry Cohn, Microsoft Research New England.
Wednesday, October 14, 2009.
Symmetry and ground states of particle systems.
How much symmetry can one expect in solutions of optimization problems (such as ground states for systems of interacting particles)? In this talk we'll look at several examples from mathematics and physics. In particular, I'll explain a phenomenon I find mysterious and bothersome: in certain very special cases, often related to exceptional mathematical structures, the pair correlation function unexpectedly encodes all relevant information, while in more general cases, even higher correlation functions seem surprisingly powerless.

Percy Deift, Courant Institute.
Wednesday, October 28, 2009.
Toeplitz determinants with Fisher Hartwig singularities
The speaker will discuss recent work with A.Its and I.Krasovsky on the asymptotics of Toeplitz determinants with Fisher hartwig singularities.

Sergey Fomin, University of Michigan, Ann Arbor.
Wednesday, November 4, 2009.
Enumeration of plane curves and labeled floor diagrams
Floor diagrams are a class of weighted oriented graphs introduced by E. Brugalle and G. Mikhalkin. Tropical geometry arguments yield combinatorial descriptions of (ordinary and relative) Gromov-Witten invariants of projective spaces in terms of floor diagrams and their generalizations. In the case of the projective plane, these descriptions can be used to obtain new formulas for the corresponding enumerative invariants. In particular, we give a proof of Goettsche's polynomiality conjecture for plane curves, and enumerate plane rational curves of given degree passing through given points and having maximal tangency to a given line. On the combinatorial side, we show that labeled floor diagrams of genus 0 are equinumerous to labeled trees, and therefore counted by the celebrated Cayley's formula. The corresponding bijections lead to interpretations of the Kontsevich numbers (the genus-0 Gromov-Witten invariants of the projective plane) in terms of certain statistics on trees.
This is joint work with Grisha Mikhalkin.

Irina Mitrea, Worcester Polytechnic Institute.
Wednesday, November 11, 2009.
Fredholm Theory for Higher Order Elliptic Boundary Value Problems.
In this talk I will briefly review the Fredholm theory approach for second order elliptic boundary value problems in $C^1$ domains and I will discuss a number of obstacles, which are due to the intricacies of the higher order setting, that have been recently overcome for the employment of this method for boundary value problems for higher order elliptic differential operators. This is done in a very general class of domains which is in the nature of best possible from the point of view of geometric measure theory.

Juan Souto, University of Michigan, Ann Arbor.
Wednesday, November 18, 2009.
Periodic flats in locally symmetric spaces.
It is well-known that if $M$ is a non-compact, hyperbolic surface of finite volume, then there is a compact set $K\subset M$ which intersects every curve homotopic to a geodesic. This is no longer true if $M$ is a higher rank locally symmetric space; we could say that geodesics are peripheral. The goal of the talk is to prove that periodic maximal flats are not peripheral.