Colloquia 2012-2013: Difference between revisions
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== Abstracts == | == Abstracts == | ||
=== '''Thu, Sept | === '''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) === | === '''Thu, Sept 20''': Persi Diaconis (Stanford) === | ||
''Spatial mixing: problems and progress'' | ''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. | 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. | ||
Revision as of 00:33, 28 July 2012
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) | TBA | 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 |
| 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.