Department of

# Mathematics

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

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     January 2014          February 2014            March 2014
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4                      1                      1
5  6  7  8  9 10 11    2  3  4  5  6  7  8    2  3  4  5  6  7  8
12 13 14 15 16 17 18    9 10 11 12 13 14 15    9 10 11 12 13 14 15
19 20 21 22 23 24 25   16 17 18 19 20 21 22   16 17 18 19 20 21 22
26 27 28 29 30 31      23 24 25 26 27 28      23 24 25 26 27 28 29
30 31


Monday, February 10, 2014

3:00 pm in 145 Altgeld Hall,Monday, February 10, 2014

#### Real slices of the moduli space of Higgs bundles

###### Laura Schaposnik Massolo (UIUC Math)

Abstract: After introducing Higgs bundles and their moduli space, through the natural hyperkähler structure of the moduli space of Higgs bundles for complex groups we shall construct three anti-holomorphic involutions whose fixed points in the moduli space give branes in the A-model and B-model. After defining what those branes are, we shall attempt to relate them to log-symplectic structures and their invariants.

4:00 pm in 241 Altgeld Hall,Monday, February 10, 2014

#### Rigidity of higher rank abelian actions

###### Zhiren Wang (Yale University)

Abstract: A $Z$-action generated by a single toral automorphism is not rigid, in the sense that invariant measures and subsets can behave quite arbitrarily. However, this is not the case for generic $Z^r$-actions by toral automorphisms. In this talk, we will describe rigidity properties of algebraic $Z^r$-actions on nilmanifolds in the categories of measures, subsets and smooth structures. We show that, up to smooth conjugacy, all Anosov $Z^r$-actions without rank-one actions on tori and nilmanifolds act by automorphisms. We will also explain how one can establish similar rigidity statements for actions by higher rank lattices by studying their abelian subgroups. This talk is partially based on joint works with Aaron Brown and Federico Rodriguez Hertz.

4:00 pm in 143 Altgeld Hall,Monday, February 10, 2014

#### Introduction to super Yang-Mills theories

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

Abstract: In this initial talk, I will start with a sampling of reasons why this topic is of interest to modern geometers and theoretical physicists. Then I will introduce Yang-Mills theory in arbitrary dimension, then supersymmetry in dimensions up to 10, and finally super Yang-Mills in dimensions 3,4,6, and 10 along with dimensional reduction. Most ideas will be discussed twice, starting with the language of physics, then reformulating in the language of mathematics with an emphasis on geometry. An additional goal of the talk is to establish interdisciplinary dialogue, so the quantity of material that actually gets covered could get reduced if necessary to promote such dialogue.

5:00 pm in 241 Altgeld,Monday, February 10, 2014