Spring 2026
Time & Location: All talks are on Wednesday in different places, at 3:00 PM .
Organizer: Katerina Gkogkou and Ken McLaughlin
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January 12, 2026
Integrability and Beyond
Topic: Soliton gas description of modulational instability
Speaker: Thibault Congy - Northumbria University, Newcastle, U.K.
Abstract: Soliton gases are infinite random ensembles of interacting solitons whose large-scale dynamics are governed by the elementary two-soliton collisions. By applying the spectral theory of soliton gases to the focusing nonlinear Schrödinger equation (fNLSE), we can describe the statistically stationary and spatially homogeneous integrable turbulence that emerges at large times from the spontaneous (noise-induced) modulational instability of the plane-wave and the elliptic “dn” solutions.
I will show that a special, critically dense soliton gas—the bound-state soliton condensate—provides an accurate model for the asymptotic state of both plane-wave and elliptic integrable turbulence. Moreover, certain statistical moments of the resulting turbulence can be computed analytically, allowing us to assess deviations from Gaussianity. These analytical predictions demonstrate excellent agreement with direct numerical simulations of the fNLSE.
The talk is based on the recent works:
“Statistics of Extreme Events in Integrable Turbulence”, T. Congy, G. A. El, G. Roberti, A. Tovbis, S. Randoux, and P. Suret, Phys. Rev. Lett. 132, 207201 (2024).
“Spontaneous modulational instability of elliptic periodic waves: The soliton condensate model”, D. S. Agafontsev, T. Congy, G. A. El, S. Randoux, G. Roberti, and P. Suret, Physica D 134956 (2025).
Location: Gibson Hall 126A
Time: 3:00
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February 02, 2026
Integrability and Beyond
Topic: The (random) matrix
Speaker: Guido Mazzuca - Tulane University
Abstract:
"Red or blue pill?" Ioana asked the graduate student.
"What happens if I take the blue one?"
"Nothing," Alan replied. "The story ends. We will know that you are not curious enough, or that you think that finding the energy levels for charged atoms is not an important quest for physics."
"Or that you do not believe in the power of probability theory, only in the crude Riemann-Hilbert method," Ioana pressed.
The student was a bit perplexed: he hated RHP, but at the same time, their quest looked impossible without it. "So if I take the red one? What is going to happen?"
"Well," said Ioana, smiling, "you will start an amazing journey. You will uncover a world of beauty and possibility. We start with the simplest possible situation: we consider a symmetric random matrix with Gaussian entries and we will compute the joint probability density function of the eigenvalues explicitly. During this journey, we will learn how to tridiagonalize a matrix, how to use recurrence relations to express the Vandermonde determinant, and much more."
Alan stood up. "And the best of all? It is going to be a symphony where all the players play their part flawlessly."
The grad took the red pill and ate it. "Well, let's get started!"
Reference: "Matrix Models for Beta Ensembles" Ioana Dumitriu, Alan Edelman https://arxiv.org/abs/math-ph/0206043
Location: TBA
Time: 3:00
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