Department of

Mathematics


Seminar Calendar
for events the day of Monday, October 28, 2013.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, October 28, 2013

10:00 am in 145 Altgeld Hall,Monday, October 28, 2013

All boundaries of contact type can keep secrets

Ely Kerman (UIUC Math)

Abstract: Let $(M, \omega)$ be a symplectic manifold with nonempty boundary, $W$. The restriction of $\omega$ to $W$, $\omega_W$, has a one dimensional kernel which defines the characteristic foliation of $W$. If $W$ is a boundary of contact type then it admits a tubular neighborhood comprised of hypersurfaces whose characteristic foliations are all conjugate to those of $W$. Since these hypersurfaces lie in the interior one might guess (or hope) that the interior of $(M, \omega)$ determines $omega_W$ or at least some of its symplectic invariants. Several questions in this direction were raised by Eliashberg and Hofer in the early nineties. In this talk I will describe the resolution of some of these questions. I will prove that neither $\omega_W$ or its action spectrum is determined by the interior of $(M, \omega)$. This involves the construction of a new dynamical symplectic plug. The construction uses only soft techniques (Moser's method) and so should hopefully be accessible to all.

4:00 pm in 241 Altgeld Hall,Monday, October 28, 2013

Hodge theory and rigidity in Teichmuller dynamics

Simion Filip (University of Chicago)

Abstract: I will start by introducing the basic concepts of Teichmuller dynamics. While many questions are of intrinsic interest, they also have direct applications to more classical systems such as polygonal billiards and interval exchanges. I will then discuss some connections to algebraic geometry and how techniques from Hodge theory can give rigidity results for dynamics.

4:00 pm in 243 Altgeld Hall,Monday, October 28, 2013

To Be Announced

Scott Ahlgren (U of Illinois), Tony Bedenikovic (Bradley U), Emily Dryden (Bucknell U)

Abstract: All graduate students are welcome to this informal panel discussion about academic careers. The panelists have expertise in a variety of types of institution - ask them whatever is on your mind! Refreshments to follow the panel.

5:00 pm in 241 Altgeld,Monday, October 28, 2013

Explicit Kazhdan constants for some property (T) group inclusions (following Shalom)

Stephen Longfield (UIUC Math)