Colloquia 2012-2013

Mathematics Colloquium

All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.

Fall 2012

date	speaker	title	host(s)
Sept 14	Jordan Ellenberg (Madison)	FI-modules: an introduction	local
Sept 20, 4pm	Persi Diaconis (Stanford)	Spatial mixing: problems and progress	Jean-Luc
Sept 21	Joyce McLaughlin (RPI)	TBA	WIMAW
Sept 28	Eric Marberg (MIT)	TBA	Isaacs
Oct 12	Joachim Rosenthal (Univ. of Zurich)	TBA	Boston
Oct 19	Irene Gamba (Univ. of Texas)	TBA	WIMAW
Oct 26	Luke Oeding (UC Berkeley)	TBA	Gurevich
Tues, Oct 30	Andrew Majda (Courant)	TBA	Smith, Stechmann
Thurs, Nov 1	Peter Constantin (Princeton)	TBA	Distinguished Lecture Series
Nov 2	Peter Constantin (Princeton)	TBA	Distinguished Lecture Series
Nov 9 and later	Reserved for potential interviews

Spring 2013

date	speaker	title	host(s)
Feb 15	Eric Lauga (UCSD)	TBA	Spagnolie
March 22	Neil O'Connell (Warwick)	TBA	Timo Seppalainen

Abstracts

Thu, Sept 14: Jordan Ellenberg (UW-Madison)

FI-modules: an introduction (joint work with T Church, B Farb, R Nagpal)

In topology and algebraic geometry one often encounters phenomena of _stability_. A famous example is the cohomology of the moduli space of curves M_g; Harer proved in the 1980s that the sequence of vector spaces H_i(M_g,Q), with g growing and i fixed, has dimension which is eventually constant as g grows with i fixed.

In many similar situations one is presented with a sequence {V_n}, where the V_n are not merely vector spaces, but come with an action of S_n. In many such situations the dimension of V_n does not become constant as n grows -- but there is still a sense in which it is eventually "always the same representation of S_n" as n grows. The preprint

http://arxiv.org/abs/1204.4533

shows how to interpret this kind of "representation stability" as a statement of finite generation in an appropriate category; we'll discuss this set-up and some applications to the topology of configuration spaces, the representation theory of the symmetric group, and diagonal coinvariant algebras. Finally, we'll discuss recent developments in the theory of FI-modules over general rings, which is joint work with (UW grad student) Rohit Nagpal.

Thu, Sept 20: Persi Diaconis (Stanford)

Spatial mixing: problems and progress

One standard way of mixing (cards, dominos, Mahjong tiles) is to 'smoosh' them around on the table with two hands. I will introduce some models for this, present data (it's surprisingly effective) and some first theorems. The math involved is related to fluid flow and Baxendale-Harris random homeomorphisims.