Department of

Mathematics


Seminar Calendar
for events the day of Thursday, April 17, 2014.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, April 17, 2014

11:00 am in 241 Altgeld Hall,Thursday, April 17, 2014

Integral structures on de Rham cohomology

Andrew Snowden (Univ. Michigan Math)

Abstract: Give a smooth projective variety X over the function field K of a complex curve C, its algebraic de Rham cohomology forms a finite dimension K vector space. This vector space can be canonically realized as the generic fiber of a coherent sheaf on C, in two ways: one Hodge-theoretic and one geometric. I will explain an arithmetic version of this, where K is a number field. Here, p-adic Hodge theory takes the place of usual Hodge theory. This is joint work with Bhargav Bhatt.

1:00 pm in Altgeld Hall 347,Thursday, April 17, 2014

Patterson-Sullivan currents, generic stretch factors and the asymmetric Lipschitz metric for Outer space

Ilya Kapovich (UIUC Math)

Abstract: We quantitatively relate the Patterson-Sullivant currents to the asymmetric Lipschitz metric on Outer space and to Guirardel's intersection number. As an application we show that for any N\ge 2 there exists a positive constant C_N>0 such that for every \phi\in Out(F_N), where F_N=F(A)=F(a_1,..,a_N) is the free group of rank N, we have $C_N\le \lambda_A(\phi)/ \Lambda_A(\phi) \le 1$. Here $\Lambda_A(\phi)= \sup_{w\ne 1} ||\phi(w)||_A/||w||_A$ is the "extremal distortion" of $\phi$, and $\lambda_A(\phi)$ is the "generic stretching factor" of $\phi$, that is, $\lambda_A(\phi)$ is the asymptotic distortion $||\phi(w)||_A/||w||_A$ where $w$ is a "long random element" in $F(A)$, as $||w||_A\to\infty$. The talk is based on joint work with Martin Lustig.

3:00 pm in 243 Altgeld Hall,Thursday, April 17, 2014

Asymptotics of equivariant syzygies

Xin Zhou (University of Michigan, Ann Arbor)

Abstract: Recent results on syzygies concentrate on their asymptotics. In this talk, I will discuss results on the asymptotics of syzygies under group actions. In particular, we study two cases. When the underlying space is the projective space, we give the asymptotic growth of syzygy modules with respect to the general linear group. When the underlying space is a toric variety, we give a sharp asymptotic description of the distribution of torus weights.

4:00 pm in 245 Altgeld Hall,Thursday, April 17, 2014

Spring Department Faculty Meeting

Abstract: The Spring Department Faculty Meeting will be held at 4 p.m. in 245 Altgeld Hall, followed by a reception in 243 Altgeld Hall.