Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, December 7, 2016.

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Wednesday, December 7, 2016

3:00 pm in 241 Altgeld Hall,Wednesday, December 7, 2016

#### The Peterson variety and the wonderful compactification

###### Ana Balibanu (University of Chicago)

Abstract: We look at the centralizer in a complex semisimple algebraic group $G$ of a regular nilpotent $e\in \operatorname{Lie}(G)$ and show that its closure in the wonderful compactifi cation $\overline{G}$ is isomorphic to the Peterson variety. We generalize this result to show that for any regular $x\in \operatorname{Lie}(G)$, the closure of the centralizer $G^x$ in $\overline{G}$ is isomorphic to the closure of a general $G^x$-orbit in the flag variety. We consider the family of all such centralizer closures and show that it has a natural Poisson structure.