Department of

# Mathematics

Seminar Calendar
for events the day of Monday, November 4, 2019.

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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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Monday, November 4, 2019

3:00 pm in 441 Altgeld Hall,Monday, November 4, 2019

#### Atiyah-Segal completion theorem

###### Tsutomu Okano (UIUC Math)

Abstract: In this talk I will walk through Atiyah and Segal's "Equivariant K theory and completion". The main result is a nice proof of the so-called Atiyah-Segal completion theorem, which relates the equivariant K theory of a G-space with the K theory of its homotopy orbit. Towards the end, I will also discuss the algebraic analogue of this result.

3:00 pm in 243 Altgeld Hall,Monday, November 4, 2019

#### Toric degeneration and symplectic rigidity

###### Susan Tolman (Illinois)

Abstract: This talk is based on joint work with Milena Pabiniak. We say that a family of symplectic manifolds satisfies symplectic rigidity if they are classified up to symplectomorphism by their cohomology ring and the cohomology class of the symplectic form. We show how toric degeneration can be used to construct new symplectomorphisms between certain smooth toric manifolds, and then use this to show that symplectic rigidity holds for a large family of Bott manifolds.

5:00 pm in 241 Altgeld Hall,Monday, November 4, 2019

#### The Dixmier trace

###### Haojian Li (University of Illinois at Urbana-Champaign)

Abstract: I would introduce pseudo-differential operators and noncommutative residues. The calculus of pseudo-differential operators is the prototype of Alain Connes' quantum calculus in noncommutative geometry. Mariusz Wodzicki defined the non-commutative residue on the classical compactly supported pseudo differential operators by integrating the principal symbol. Connes gave the first result to identify Wodzicki residue with a singular trace, i.e., so-called Dixmier trace. This result is considered as the foundation of the noncommutative geometry.