Department of

# Mathematics

Seminar Calendar
for events the day of Monday, November 10, 2014.

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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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30


Monday, November 10, 2014

3:00 pm in 341 Altgeld Hall,Monday, November 10, 2014

#### Metrics on Stacks

###### Matias del Hoyo (IMPA)

Abstract: The Linearization Theorem for Lie groupoids provides an organizing framework for classic results on the geometry of fibrations, actions and foliations. It was conjectured by A. Weinstein, who also gave a Morita invariance argument reducing the problem to the fixed point case, later solved by N. Zung. In a joint work with R. Fernandes we approach the linearization problem from a new perspective, developing a notion of metrics on Lie groupoids, achieving a simpler proof and a stronger theorem. Morita invariance is not needed in our approach, but a version of it still holds, leading to a definition of metrics on stacks. I will recall the interplay between groupoids and stacks, discuss the theory of Riemannian groupoids, and present some of our next results.

4:00 pm in 243 Altgeld Hall,Monday, November 10, 2014

#### G-spectra Episode V: The Fixed Points Strike Back

###### Cary Malkiewich (UIUC Math)

Abstract: It's time for us to begin the Jedi training with the true definitions of orthogonal G-spectra, genuine fixed points, and geometric fixed points. Our motivation will be understanding the equivariant structure on THH, although there are many other applications of this theory. I'll begin by reviewing a straightforward but naive construction of the genuine equivariant category and discussing its shortcomings. Then we'll move on to a richer category that does not have those shortcomings. The definitions are about as painful as being frozen in carbonite, but we'll try to move on quickly to consequences that are useful for calculation, like the Adams isomorphism, the tom Dieck splitting, and the norm cofibration sequence. There will be examples.

5:00 pm in Altgeld Hall,Monday, November 10, 2014

#### Grothendieck's theorem following Pisier-Shlyakhtenko

###### Li Gao (UIUC)

Abstract: We will give an outline of the main arguments following Pisier-Shlyakhtenko's original proof.