Research Seminar: Integrability and Beyond

Spring 2025

Time & Location: All talks are on Wednesday in different places,  at 3:00 PM .
Organizer: Katerina Gkogkou and Ken McLaughlin

Archives

 

 

January 27, 

Topic:  Random Matrices: Fredholm determinant representations for (a) spectral gaps, (b) largest eigenvalues, and (c) number statistics.
Ken McLaughlin - Tulane University

Abstract:  How to compute interesting statistical quantities in random matrices: Fredholm determinant representations for (a) spectral gaps, (b) largest eigenvalues, and (c) number statistics.

With the assistance of the whole group, this should be very introductory.

Speakers: to be determined, starting with Ken McLaughlin on January 27.

 

Location: Gibson Hall 310
Time: 3:00 PM

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February 3, 

Topic:  Random Matrices: Fredholm determinant representations for (a) spectral gaps, (b) largest eigenvalues, and (c) number statistics.
Ken McLaughlin - Tulane University

Abstract:  We will start calculating some basic number statistics for finite sized random matrices using Hermite polynomials, and compare to numerical experiments. In the second half, I will explain the connection between random matrices and Hermite polynomials.
 

Location: Gibson Hall 310
Time: 3:00 PM

 

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February 10, 

Topic:  Random Matrices: Fredholm determinant representations for (a) spectral gaps, (b) largest eigenvalues, and (c) number statistics.
Ken McLaughlin - Tulane University

Abstract:  We will continue exploring the connection between random matrices and Hermite polynomials, and start the proof of the relation between eigenvalue probabilities and Fredholm determinants. Time permitting, we will return to the numerical experiments, to carefully develop intuition.
 

Location: Gibson Hall 310
Time: 3:00 PM