[Binghamton Geometry/Topology Seminar] Geometry & Topology Seminar

[somnath at math.binghamton.edu]

BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR

*Date:*  Thursday, May 8th, 2014

*Time:*  2:50-3:50pm
*Place:*  Library North 2205 followed by coffee/tea in the Anderson
Reading Room.

*Speaker: ** *Rita Jimenez Rolland (Northeastern University)
*Title: * The cohomology of M_{g,n} and other representation stability
phenomena

*Abstract:* Let M_{g,n} be the moduli space of genus g Riemann surfaces
with n marked points. Given a non negative integer i, we want to
understand how the i-th rational cohomology group of M_{g,n} changes as
the parameter n increases. It turns out that the symmetric group S_n acts
on it and the sequence of S_n-representations ``stabilizes'' in a certain
sense once n is large enough. In this talk I will explain the behavior of
this and other examples via the language of representation stability.
Moreover, I will introduce the notion of a finitely generated FI-module
and show our sequence of interest has this underlying structure which
explains the stability phenomena mentioned above. As a consequence we
obtain that, for n large enough with respect to i, the i-th Betti number
of M_{g,n} is a polynomial in n of degree at most 2i.