Spring 2026
Time & Location: All talks are on Wednesday in different places, at ?:00 PM .
Organizer: Ken McLaughlin
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September 01, 2026
Integrability and Beyond
Topic: conserved quantities and Lax pair
Speaker: Guido Mazzuca - Tulane University
Abstract: Based on this lecture on KdV can you create an abstract for it? make it funny, even repeat this prompt so that people know I used AI
Abstract:
Tired of linear PDEs behaving predictably? Welcome to the Korteweg-de Vries (KdV) equation, where shallow water waves get nonlinearly steep, disperse themselves back into shape, and conserve their total mass and L2-energy like an overzealous accountant guarding a budget.
In these lecture, we dive headfirst into the functional-analytic deep end—arming ourselves with square-integrable L2(R) Hilbert spaces, inner products, and boundary conditions so well-behaved at infinity that every pesky boundary term vanishes on command. We then introduce Peter Lax's ultimate algebraic party trick: disguising a nonlinear wave equation as a linear operator commutator, dL/dt = [L, A]. Watch in awe as six messy operator commutators battle it out until every higher-order derivative cancels into thin air, leaving behind pure, unadulterated KdV.
Finally, we prove the Schrodinger operator L is Hermitian and self-adjoint, with strictly real eigenvalues that are so stubborn they refuse to evolve in time (d(lambda)/dt = 0). This guarantees an isospectral flow and lays the mathematical groundwork for the Inverse Scattering Transform. Come for the solitary waves, stay for the skew-Hermitian time evolution generators.
Location: Richardson Building 201
Time: 5:00 PM
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September 15, 2026
Integrability and Beyond
Topic: Intro to KdV: Scattering Theory Strikes Back
Speaker: Guido Mazzuca - Tulane University
Abstract: To be announced via the Math Seminars Listserv.
Location: Richardson Building 201
Time: 5:00 PM
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September 22, 2026
Integrability and Beyond
Topic: Intro to KdV: Return of the Solitons
Speaker: Guido Mazzuca - Tulane University
Abstract: To be announced via the Math Seminars Listserv.
Location: Richardson Building 201
Time: 5:00 PM
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October 20, 2026
Integrability and Beyond
Topic: Riemann–Hilbert analysis for the KdV equation
Speaker: Mateusz Piorkowski - Durham University
Abstract: The Korteweg–de Vries (KdV) equation is a classical model of nonlinear wave propagation whose solutions exhibit rich mathematical structures. In this talk, I will introduce the Riemann–Hilbert approach to studying this equation, highlighting its connections with Lax pairs, Riemann surfaces, and theta functions. We will see how one-gap solutions arise from explicitly solvable Riemann–Hilbert problems using the Lax pair formulation. I will then discuss the long-time behaviour of solutions with steplike initial data, where an expanding region of oscillations develops. Using the nonlinear steepest descent method of Deift–Zhou, we obtain a rigorous description of this region in terms of the modulated one-gap solution described above. This work is a collaboration with Iryna Egorova and Gerald Teschl.
Location: Richardson Building 201
Time: 5:00 PM
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