Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, March 5, 2014.

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30 31


Wednesday, March 5, 2014

3:00 pm in 145 Altgeld Hall,Wednesday, March 5, 2014

#### Parity sheaves on the affine Grassmannian and the Mirkovic-Vilonen conjecture

###### Laura Rider (MIT)

Abstract: Let G be a connected complex reductive group, and let Gr denote its affine Grassmannian. The topology of Gr encodes the representation theory of the split Langlands dual group over any field via the geometric Satake equivalence due to Mirkovic--Vilonen. This result raises the possibility of using the universal coefficient theorem of topology to compare representations over different fields. With that in mind, Mirkovic and Vilonen conjectured that the local intersection cohomology of the affine Grassmannian with integer coefficients is torsion-free. I will discuss the proof of (a slight modification of) the Mirkovic-Vilonen conjecture. This is joint work with Pramod Achar.

4:00 pm in 245 Altgeld Hall,Wednesday, March 5, 2014

#### The Fourteenth Problem of Hilbert

###### William Haboush (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: I will describe what, in the nineteenth century, was called the fundamental problem of invariant theory and Hilbert’s solution to that problem and its implications for modern mathematics. Then I will state the fourteenth problem of Hilbert, which was a conjectural generalization of his solution to the fundamental problem of invariant theory, and give a history of the gradual solution to the problem. I will try to give some sense of the applications of these results to contemporary algebraic geometry.