Department of

# Mathematics

Seminar Calendar
for events the day of Monday, March 3, 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.
    February 2014            March 2014             April 2014
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Monday, March 3, 2014

3:00 pm in 145 Altgeld Hall,Monday, March 3, 2014

#### Folded Symplectic Reduction

###### Daniel Hockensmith (UIUC Math)

Abstract: The Marsden-Weinstein-Meyer reduction theorem is an indispensable tool for the study of Hamiltonian group actions on symplectic manifolds. It gives an explicit recipe for the construction of a symplectic reduced space using only regular values of the moment map and the group action. I will prove that if one replaces symplectic manifolds with oriented, folded-symplectic manifolds in the statement of the MWM reduction theorem then a reduced space with a natural folded-symplectic form is obtained in the same way. I will then argue that the assumptions of this generalized theorem are too strong, leading us towards a more robust set of assumptions for a folded-symplectic reduction theorem.

4:00 pm in 143 Altgeld Hall,Monday, March 3, 2014

#### Kahler geometry and supersymmetry

###### Sheldon Katz (Illinois Math)

Abstract: I begin by discussing the relationship between N=1 chiral fields in 4 dimensions and holomorphic functions, then show how Kahler manifolds naturally arise in 4-dimensional supersymmetric theories. This is the first instance we are considering of a more general phenomenon: the relationship between vacuum expectation values of neutral scalar fields, and the moduli space of the theory.

4:00 pm in 241 Altgeld Hall,Monday, March 3, 2014

#### GL(2,R) orbit closures of translation surfaces

###### Alex Wright (University of Chicago)

Abstract: We will survey recent results towards the classification of GL(2,R) orbit closures of translation surfaces, including the technique of cylinder deformations and the author's joint results with Aulicino and Nguyen in genus 3.

5:00 pm in 241 Altgeld Hall ,Monday, March 3, 2014

#### Free Monotone Transport, Part 1

###### Michael Brannan (UIUC Math)

Abstract: I will discuss the recent paper of A. Guionnet and D. Shlyakhtenko with the same title.