Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, August 28, 2013.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, August 28, 2013

3:00 pm in 143 Altgeld Hall,Wednesday, August 28, 2013

#### Whittaker functions and Toda equations for SL(2)

###### Rinat Kedem (UIUC)

Abstract: This will be an organizational/introductory meeting to the new incarnation of the representation theory seminar. Topics for this semester will be mostly related to combinatorial representation theory in the sense of integrable difference/differential equations, fermionic character formulas, symmetric functions and the AGT correspondence. The first talk will be geared towards graduate students and requires no prior knowledge whatsoever. I will explain what a Whittaker vector is and why Whittaker functions satisfy differential equations using a completely explicit example.

4:00 pm in 245 Altgeld Hall,Wednesday, August 28, 2013

#### The Laplacian, waves, and open problems in geometric spectral theory

###### Richard Laugesen (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: Why does the Laplacian appear in all the major equations of classical and quantum physics? Is there a formula for approximating frequencies of standing waves? Does geometry constrain physics? We embark on a gentle and incomplete tour motivated by these questions, and run into several open problems for eigenvalues of the Laplacian.