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Mini-course by Paul Wiegmann: Selberg Integrals and Their Applications to Conformal Field Theory, Quantum Hall Effect and Hydrodynamics.

First lecture: May 8, 2018, 2:15pm-3:30pm in SCGP Room 313
Full schedule of following lectures can be found below:
 
Paul Wiegmann (University of Chicago)
 
Title: Selberg integrals and their applications to conformal field theory, quantum Hall effect and hydrodynamics.
Abstract:
Seemingly different phenomena such as quantum Hall effect, superfluids, instabilities in hydrodynamics, models of unstable growth (such as Hele-Shaw problem) have common geometric properties.  They could be studied on a unified platform based on Selberg integrals with large number of variables.
In the series of talks I will review recent advances in some of these fields emphasizing their common geometric aspects.
 
Synopsis 

Lecture 1 (Tuesday, May 8, 14.30):

Selberg integral, history, generalizations, applications. Selberg integral on Riemann surfaces.
 
Lecture 2 (Monday, May 14, 10.30): 
 
Selberg integral with large number of variables as quantum field theory.
 
Lecture 3  (Monday, May 21, 10.30):: 
 
Selberg integrals and gravitational anomaly. Application to Hydrodynamics.
 
Lecture 4 (Tuesday, June 5, 10.30): 
 
Applications of Selberg Integrals to hydrodynamics (continue).
 
Lecture 5: (Tuesday, June 12, 10.30): 
 
Hele-Shaw problem, Boutroux curves  and patterns  of zeros of biorthogonal polynomials.