Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, December 7, 2005.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, December 7, 2005

2:00 pm in 347 Altgeld Hall,Wednesday, December 7, 2005

#### Continuous Hecke algebras

###### Wee Liang Gan (MIT)

Abstract: Drinfeld introduced the family of degenerate affine (graded) Hecke algebras attached to any finite group G and its linear finite dimensional complex representation V. I will speak on the continuous'' generalization of these algebras, in which the group G is a reductive algebraic group, and V is its algebraic representation. We call this generalization continuous Hecke algebras. They include continuous generalizations of symplectic reflection algebras and rational Cherednik algebras. A motivation for studying continuous Hecke algebras comes from the fact that their representation theory (which is yet to be developed) unifies the representation theories of real reductive groups, Drinfeld-Lusztig degenerate affine Hecke algebras, and symplectic reflection algebras of (in particular, rational Cherednik algebras). This is a joint work with Etingof and Ginzburg.

3:00 pm in 441 Altgeld Hall,Wednesday, December 7, 2005

#### An Introduction to Orbifolds and Groupoids

###### Nora Ganter (UIUC Math)

Abstract: Following an introductory paper by Moerdijk, I will explain what an orbifold is.

4:00 pm in 245 Altgeld Hall,Wednesday, December 7, 2005

#### Enumerative Algebraic Geometry

###### Sheldon Katz (Dept. of Mathematics, UIUC)

Abstract: How many lines pass through two given points of the plane? This is a typical (although trivial) question of enumerative geometry. In this talk, I start with an intuitive approach to enumerative geometry and let this lead naturally to considerations of modern algebraic geometry, algebra, and topology. Some newer ideas inspired by string theory will be considered as well.