Department of

# Mathematics

Seminar Calendar
for events the day of Monday, April 28, 2014.

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events for the
events containing

More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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1          1  2  3  4  5                1  2  3
2  3  4  5  6  7  8    6  7  8  9 10 11 12    4  5  6  7  8  9 10
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Monday, April 28, 2014

3:00 pm in Altgeld Hall,Monday, April 28, 2014

#### Lie algebra cohomology and a degenerate cup product on the flag manifold

###### Sam Evens (Notre Dame)

Abstract: Belkale and Kumar introduced a degeneration of the usual cup product on $H^*(G/P)$ which gives an optimal solution to the geometric Horn problem. In this talk, I will explain joint work with Bill Graham where we realize the Belkale-Kumar product using relative Lie algebra cohomology. We do this using a family in the variety of Lagrangian subalgebras.

4:00 pm in 143 Altgeld Hall,Monday, April 28, 2014

#### A gauge-theoretic "derivation" of Geometric Langlands

###### Sheldon Katz (Illinois Math)

Abstract: I describe N=4 super Yang-Mills in 4 dimensions and its GL twist which allows the theory to be defined on a compact 4 manifold M. Taking M to be a product $\Sigma\times C$ of Riemann surfaces leads to an effective two-dimensional sigma model on $\Sigma$ with target space $M_H(C,G)$, the Hitchin moduli space for C with gauge group G. S-duality takes this sigma model to a "mirror" sigma model on $M_H(C,^{\rm L}G)$, where $^{\rm L}G$ is the Langlands dual group. The Geometric Langlands correspondence results readily from the mathematical interpretation of this duality.

5:00 pm in 241 Altgeld,Monday, April 28, 2014