Department of

Mathematics


Seminar Calendar
for events the day of Wednesday, March 18, 2015.

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Wednesday, March 18, 2015

11:00 am in 443 Altgeld Hall,Wednesday, March 18, 2015

The classification of analytic functors from based spaces to spectra

Michael Ching (Amherst)

Abstract: The goal of this talk is to understand the comonad that acts on the derivatives of a functor from based spaces to spectra. On the one hand, this comonad captures the structure of a `divided power' module over the Lie operad. I will give a different description in terms of the Koszul duals of the E_n-operads. In particular, the partially-stabilized cross-effects of such a functor have an action by K(E_n). Taking the colimit we get a comonad that acts on the derivatives themselves. Underlying this construction is a theory of Koszul duality for modules over operads of spectra. This is joint work with Greg Arone.

1:00 pm in 343 Altgeld Hall,Wednesday, March 18, 2015

Steiner's formula in the Heisenberg Group

Kevin Wildrick (Montana State University)

Abstract: Steiner's formula states that the volume of an epsilon neighborhood of sufficiently smooth set in n- dimensional Euclidean space is a polynomial of degree n, whose coefficients carry information about the curvature of the boundary of the set. We will provide an analogous result for the Carnot-Carathéodory distance in the first Heisenberg group. Although the resulting function is not, in general, a polynomial, it is analytic and the coefficients in its series expansion are integrals of second order differential operators. In particular, this approach produces a candidate for the notion of "horizontal Gauss curvature" in the Heisenberg group.

4:00 pm in 245 Altgeld Hall,Wednesday, March 18, 2015

Triangles and the theta series

James Pascaleff (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: There is an interesting relationship between the areas of triangles in the two-torus with boundary on three circles and the terms in the theta series $\theta(z,q) = \sum_{n=-\infty}^\infty q^{n^2}z^n$. I will explain this and use it as a gentle introduction to the phenomenon of mirror symmetry.