Department of

Mathematics


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

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Questions regarding events or the calendar should be directed to Tori Corkery.
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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.