Department of

# Mathematics

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

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    February 2015            March 2015             April 2015
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5  6  7    1  2  3  4  5  6  7             1  2  3  4
8  9 10 11 12 13 14    8  9 10 11 12 13 14    5  6  7  8  9 10 11
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22 23 24 25 26 27 28   22 23 24 25 26 27 28   19 20 21 22 23 24 25
29 30 31               26 27 28 29 30



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.