Department of

# Mathematics

Seminar Calendar
for events the day of Monday, March 28, 2016.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    February 2016            March 2016             April 2016
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1  2  3  4  5  6          1  2  3  4  5                   1  2
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Monday, March 28, 2016

2:00 pm in 345 Altgeld Hall,Monday, March 28, 2016

#### The Intricate Maze of Graph Complexes

###### Vasily Dolgushev   [email] (Temple University)

Abstract: In the paper “Formal noncommutative symplectic geometry”, Maxim Kontsevich introduced three versions of cochain complexes GC_Com, GC_Lie and GC_As “assembled from” graphs with some additional structures. The graph complex GC_Com (resp. GC_Lie, GC_As) is related to the operad Com (resp. Lie, As) governing commutative (resp. Lie, associative) algebras. Although the graphs complexes GC_Com, GC_Lie and GC_As (and their generalizations) are easy to define, it is hard to get very much information about their cohomology spaces. In my talk, I will describe the links between these graph complexes (and their modifications) to the cohomology of the moduli spaces of curves, the group of outer automorphisms Out(F_r) of the free group F_r on r generators, the absolute Galois group Gal(bar{Q}/Q) of rationals, finite type invariants of tangles, and the homotopy groups of embedding spaces.

4:00 pm in 245 Altgeld Hall,Monday, March 28, 2016

#### Geometry and Representation Theory

###### Thomas Nevins (Department of Mathematics, University of Illinois)

Abstract: Symmetry is ubiquitous in geometry and physics. Representation theory studies the algebraic shadow of geometric symmetry, in (loose) analogy with the way (co)homology theory studies the algebraic shadow of topology. I will introduce a few basic ideas and examples of representation theory, explain modern approaches to their study, and indicate at least one direction of contemporary research. Much of the talk will rely only on calculus and linear algebra.

5:00 pm in 241 Altgeld Hall ,Monday, March 28, 2016

#### Quantum Expander (Continued)

###### Li Gao (UIUC Math)

Abstract: I will continue to present G.Pisier's work on quantum expander. One main result is that the number of "δ-separated" quantum expanders grows as exp(n^2), where n is the dimension of matrix. I will also outline some the applications in operator space.