Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, January 19, 2005.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, January 19, 2005

3:00 pm in 341 Altgeld Hall,Wednesday, January 19, 2005

#### Elliptic Cohomology and Derived Algebraic Geometry

###### Jacob Lurie (Harvard)

4:00 pm in 245 Altgeld Hall,Wednesday, January 19, 2005

#### Morita equivalence of noncommutative tori

###### Hanfeng Li (University of Toronto, Canada)

Abstract: Noncommutative tori are perhaps the best studied interesting examples of noncommutative differentiable manifolds. Morita equivalence is one of the basic tools in noncommutative geometry. In 1981, as one of the first applications of K-theory in noncommutative geometry, Rieffel classified 2-dimensional noncommutative tori up to Morita equivalence. In this talk I will describe several results (obtained partly in collaboration with Elliott) classifying higher-dimensional noncommutative tori at various levels: up to gauge Morita equivalence (introduced by Schwarz for applications in M theory) at the smooth algebra level, up to Morita equivalence at the smooth algebra level (in the generic case), and up to Morita equivalence at the C*-algebra level.