Fall 2026
December 7, 2026, 4:00–5:00 pm, East Hall 1866
Speaker: Yvonne Alma Bronsard (CNRS, Nantes)
Title: TBA
Abstract: TBA
November 16, 2026, 4:00–5:00 pm, zoom
Speaker: Amol Aggarwal (Stanford University)
Title: TBA
Abstract: TBA
November 2, 2026, 4:00–5:00 pm, zoom
Speaker: Adam Doliwa (University of Warmia and Mazury)
Title: TBA
Abstract: TBA
October 26, 2026, 4:00–5:00 pm, zoom
Speaker: Manuela Girotti (Emory University)
Title: Long time asymptotics of the generalized soliton gas for the mKdV equation
Abstract: We analyze a new class of solutions of the modified KdV equation introduced by Dyachenko, Zakharov, and Zakharov, and which can be interpreted as a soliton gas. These solutions are characterized by a Riemann-Hilbert problem which arises as the limit $N\to \infty$ of a sequence of $2N$-soliton RH problems, where the solitons display two different triangularity in the jumps. The limiting RH problem belongs to a novel class of problems, where the jump matrices do not have any zero entry (as opposed to the classical upper/lower triangular setting).
We show that the initial profile of such a gas solution is approaching a cnoidal wave solution for $x\to \pm \infty$ with different phase shifts, and we establish an asymptotic description of the gas of solitons for large times that is valid over the entire spatial domain, in terms of Jacobi elliptic functions, with slowly modulated phase shifts as time varies from $-\infty$ to $+\infty$.
This is a joint work with Ken McLaughlin (Tulane U.) and Robert Jenkins (UCF).
October 12, 2026, 4:00–5:00 pm, zoom
Speaker: Amari Jaconelli (University of Bristol)
Title: On Fredholm Pfaffians and Riemann-Hilbert Problems
Abstract: In this talk, I will illustrate how classes of Fredholm Pfaffians, which can describe the eigenvalue distributions for orthogonal and symplectic matrix ensembles, can be computed in terms of canonical, auxiliary Riemann-Hilbert problems.
This is done by first algebraically manipulating the kernel of the Fredholm Pfaffian and then relating the resulting Pfaffian to a Riemann-Hilbert problem, assuming its main kernel is either of additive Hankel composition or truncated Wiener-Hopf type. One can then find asymptotic results for the Fredholm Pfaffian as a natural consequence of the Riemann-Hilbert problem characterisation.
This talk is based on my paper with Thomas Bothner, currently available in preprint on the arXiv: https://arxiv.org/abs/2511.23362.
October 5, 2026, 4:00–5:00 pm, East Hall 1866
Speaker: Alexander Tovbis (University of Central Florida)
Title: Extremal Problems Motivated by Focusing NLS Condensates
Abstract: Soliton gases for integrable systems is a rapidly developing new area in the theory of nonlinear waves. For a given spectral support set, a soliton gas of maximal average intensity is called soliton condensate. A spectral support set for a fNLS soliton condensate is often represented by a finite collection of points (anchors) E ⊂ C_+, connected with each other and/or with the real axis by some set of (Schwarz symmetrical) arcs. Given a set of anchors E, a natural question is to find a collection of such arcs that produces fNLS soliton condensate of minimal average intensity. That leads to a modification of the well-known Chebotarev’s continuum problem, which consists in finding a continuum K ⊂ C of minimal logarithmic capacity that contains a given set of anchors E ⊂ C. In this talk, we discuss our solution to the modified Chebotarev’s problem, where E and K are subsets of C_+ and where we minimize the Dirichlet energy of C_+ \ K instead of the logarithmic capacity of K. This is a joint work with Marco Bertola.
September 28, 2026, 4:00–5:00 pm, zoom
Speaker: Allison Byars (University of North Carolina at Chapel Hill)
Title: Dispersive decay for the Modified Benjamin-Ono equation with small data
Abstract: We study the modified Benjamin-Ono equation for small, localized initial data where no solitons arise. Unlike the standard Benjamin-Ono equation, the modified version is not known to be completely integrable, so we cannot rely on integrable systems tools. First, to manage the nonlocal Hilbert transform in the linear part of the equation, we split it using positive and negative frequency projections. We then combine wave packet testing of Ifrim and Tataru, the Klainerman–Sobolev vector field method, a normal form transformation, and a bootstrap argument, to establish a global-in-time dispersive decay estimate.
September 21, 2026, 4:00–5:00 pm, zoom
Speaker: Linfeng Wei (Texas Tech)
Title: Difference equations of average entropies
Abstract: Exact cumulants of entanglement entropies of random state ensembles have traditionally been studied within the random matrix framework. In this talk, we propose an alternative approach based on the intrinsic connection to integrable systems. The central idea is to embed entropic quantities into tau functions satisfying Toda-type lattice equations, which in turn yield linear difference equations for their averages. Directly solving the difference equations recovers exact entropy formulas in the literature. The integrable systems approach bypasses the case-by-case, ensemble-dependent derivations required by random matrix methods. The approach also suggests a possible route towards unified and more efficient higher-order cumulant calculations by exploring integrable hierarchies.
This is joint work with Youyi Huang, Lu Wei and Peter Forrester.
September 15, 2026, 4:00–5:00 pm, zoom
Speaker: Zechuan Zhang (SISSA)
Title: Direct and Inverse Scattering on Step-like Elliptic Backgrounds and Full Soliton Gases for the Focusing NLS Equation
Abstract: In this talk, I will present direct and inverse scattering for the focusing nonlinear Schrödinger equation with initial data approaching elliptic traveling waves as \(x\to\pm\infty\). Under suitable assumptions, we characterize the scattering data and establish a uniquely solvable Riemann–Hilbert formulation. For a suitable class of reflectionless data, this formulation also arises as a continuum limit of multisoliton solutions, yielding a full soliton gas that remains nonvanishing at both spatial infinities.
This is joint work with Tamara Grava, Robert Jenkins and Xiaofan Zhang.