Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, November 9, 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, November 9, 2005

3:00 pm in 441 Altgeld Hall,Wednesday, November 9, 2005

#### Interesection Homology

###### Shivi Bansal (UIUC Math)

Abstract: We will begin with a review of some (co)homology theories like singular, simplicial, sheaf etc and some theorems like Poincare Duality valid for nonsingular spaces. By considering some examples we will see how these theorems fail to hold if the space has singularities. Intersection (co)homology (IC) provides a setting where these theorems are true even for spaces with singularities. We will conclude with a discussion of sheaf theoretic versions of IC and perverse sheaves. The talk should be of interest to survivors of courses like Algebraic Topology or any version of Algebraic Geometry.

4:00 pm in 245 Altgeld Hall,Wednesday, November 9, 2005

#### What is an algebraic group?

###### William Haboush (Dept. of Mathematics, UIUC)

Abstract: Algebraic groups are ubiquitous in geometry and topology and indeed Klein famously proposed that they determined geometry. I will try to give an idea of what they are and I will describe root systems and the Cartan Killing classification of semisimple algebraic groups and I will illustrate it with an example.