Department of

# Mathematics

Seminar Calendar
for events the day of Friday, May 2, 2014.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, May 2, 2014

4:00 pm in 345 Altgeld Hall,Friday, May 2, 2014

#### Embedding E_0

###### Slawomir Solecki (UIUC)

Abstract: We will read the paper An embedding theorem of E_0 with model theoretic applications" by Kaplan and Miller (http://arxiv.org/pdf/1308.5515v1.pdf)

4:00 pm in 347 Altgeld Hall,Friday, May 2, 2014

#### Equivariant cohomology and the moment map

###### Shiyu Shen (UIUC Math)

Abstract: This talk is based on the paper by Atiyah and Bott with the sames name as the title of this talk. Equivariant cohomology is a powerful tool to study manifolds with a group action. The localization theorem and the de Rham theorem for equivariant cohomology relate the integration of certain types of differential forms to local properties of the stationary points. In this talk, I will talk about an application of this idea in sympletic geometry and deduce the Duistermaat-Heckman formula, which asserts that the pushforward of the canonical measure on a sympletic manifold under the moment map is a piecewise polynomial measure, for the special case of sympletic circle actions with isolated fixed points. Examples will be given.