Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, February 26, 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


Wednesday, February 26, 2014

3:00 pm in 145 Altgeld Hall,Wednesday, February 26, 2014

#### Generalized Harish-Chandra Modules

###### Sarah Kitchen (University of Michigan)

Abstract: Harish-Chandra modules, together with Beilinson-Bernstein localization, are well known to allow the study of representations of real Lie groups from a complex algebraic perspective. These modules are simultaneously a representation of the complexification of the Lie algebra and maximal compact subgroup of the real group. Generalized Harish-Chandra modules weaken these requirements on the pair by taking any semi-simple complex Lie algebra, and any reductive subalgebra. In this talk, I will explain new considerations that must be taken into account in order to localize these objects and a geometric approach to a conjecture of Penkov and Zuckerman, which categorifies a parameterization of some of the irreducible modules.

4:00 pm in 245 Altgeld Hall,Wednesday, February 26, 2014

#### Symplectic Non-Squeezing and Beltrami equation

###### Alexander Tumanov (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: In his celebrated paper of 1985, Gromov developed a theory of J-complex curves as a powerful tool in symplectic geometry. One of the headlines of that paper is the Non-Squeezing Theorem. Another matter is the classical Beltrami equation, which goes back to Gauss. I will show that the two are related, in particular, how to prove Gromov's theorem by means of the Beltrami equation.