Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, February 2, 2005.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     January 2005          February 2005            March 2005
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1          1  2  3  4  5          1  2  3  4  5
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Wednesday, February 2, 2005

3:00 pm in 441 Altgeld Hall,Wednesday, February 2, 2005

#### The Étale Slice Theorem

###### Bin Wang (Dept. of Mathematics, UIUC)

Abstract: We will consider a linearly reductive group acting on an affine variety. We will prove an equivariant Zariski main theorem and show that every closed orbit has an étale neighborhood admitting a slice decomposition.

4:00 pm in 341 Altgeld Hall,Wednesday, February 2, 2005

#### Hall's theorem on finitely generated subgroups of free groups

###### Ilya Kapovich (UIUC Math)

4:00 pm in 245 Altgeld Hall,Wednesday, February 2, 2005

#### Loop spaces and Langlands duality

###### David E. Nadler (University of Chicago)

Abstract: Langlands' vision of number theory has had a tremendous impact on the representation theory and topology of loop groups. In particular, deep results about the structure of loop groups involve the Langlands dual group. In this talk, I will describe a project, joint with D. Gaitsgory (U. of Chicago), devoted to the topology of loop spaces of more general varieties with "lots of symmetry". We show that the singularities of the loop space of such a variety may be described in terms of a dual group. The dual group also governs many aspects of the original variety, such as its differential operators and compactifications. (The talk will not assume any prior knowledge.)