Winter 2026
January 26, 2026, 4:00–5:00 pm, zoom
Speaker: Aikaterini Gkogkou (Tulane University)
Title: Painlevé Universality class for the maximal amplitude solution of the Focusing Nonlinear Schrödinger Equation with randomness
Abstract: In this work, we establish universality results for the $N$-soliton solution of the focusing NLS equation at maximal amplitude. Specifically, we choose the associated normalization constants so that the solution achieves its maximal peak, which, in the large-$N$ limit, satisfies a Painlevé-type equation independently of the distribution of the (random) discrete eigenvalues. We identify two distinct universality classes, determined by the structure of the discrete eigenvalues: the \textit{Painlevé--III} and \textit{Painlevé--V} rogue-wave solutions. In the Painlevé--III case, the eigenvalues take the form $\lambda_j = v_j + i \mu_j$, while for Painlevé--V they satisfy $\lambda_j = -\zeta \, j + v_j + i \mu_j$, with $0 < \zeta < 1$. In both cases, $v_j$ and $\mu_j$ are sub-exponential random variables. Universality can then be summarized as follows: regardless of the specific realizations of the amplitudes and velocities, provided they are sub-exponential random variables and the normalization constants are chosen to maximize the \(N\)-soliton solution, the resulting maximal peak always corresponds to either a Painlevé--III or Painlevé--V rogue-wave profile in the large-$N$ limit.
February 2, 2026, 4:00–5:00 pm, zoom
Speaker: Jacek Szmigielski (University of Saskatchewan)
Title: Camassa-Holm Equations with an internal symmetry
Abstract: In the first part of my talk, I will revisit my work on the scalar Camassa–Holm equation, which will set the stage for the second part. There, I will outline a construction of spinor analogs of the Camassa–Holm equation. In essence, each orthogonal group gives rise to a Camassa–Holm–type equation with intricate internal dynamics. I will motivate this generalization using spectral deformations of the Euler–Bernoulli beam problem, which corresponds to the Clifford algebra on two generators with Minkowski signature. The dynamics of solutions of this Clifford extension are far more intricate than in the scalar case, a contrast I will illustrate with concrete examples. The talk is based on recent joint work with R. Beals and ongoing research with A. Hone and V. Novikov.
February 9, 2026, 4:00–5:00 pm, zoom
Speaker: Thierry Laurens (University of Wisconsin-Madison)
Title: Continuum Calogero--Moser models
Abstract: The focusing CCM equation is a completely integrable PDE that describes a continuum limit of a particle gas interacting pairwise through an inverse-square potential. This system is well-posed below the mass of the soliton, but above this threshold there are solutions that blow up in finite time.
The defocusing model arises as a modulation equation for internal waves in a deep stratified fluid. In this setting, it is a member of a family of systems known as the intermediate nonlinear Schrödinger equations.
In this talk, we will discuss some recent well-posedness results for the continuum Calogero--Moser and intermediate nonlinear Schrödinger equations. This is based on joint works with Andreia Chapouto, Justin Forlano, Rowan Killip, and Monica Visan.
February 16, 2026, 4:00–5:00 pm, East Hall 1866
Speaker: Kenta Miyahara (Indiana University Indianapolis)
Title: Transition Asymptotics for the Real Solutions of the sinh-Gordon Painlev\'e III
Abstract: We consider solutions of the sinh-Gordon Painlev\'e III equation
\[
u_{xx} + \frac{1}{x} u_x = \sinh u
\]
that are real on \((0, \infty)\). They are parametrized by the monodromy parameter \( p \in \overline{\mathbb C} \), \( |p|>1 \), and an additional real parameter \( s^{\mathbb R} \) when \( p=\infty \). We describe the transition between singular solutions (\( |p|<\infty \)) and smooth solutions (\( p=\infty \)), as \( x \to +\infty \) and \( p \to \infty \) given that \( 2\Im(p)=-s^\R\).
This presentation is based on the ongoing work with Maxim Yattselev.
February 23, 2026, 4:00–5:00 pm, zoom
Speaker: Matthew Mitchell (University of Central Florida)
Title: Semiclassical Soliton Ensembles for the Intermediate Long Wave and Korteweg-de Vries Equations
Abstract: Semiclassical soliton ensembles (SSE) in the small dispersion limit are initially coherent collections of many solitons that well-approximate some initial profile. Evolving forward in time, the profile will eventually undergo wave breaking, shedding the solitons and generating a dispersive shock wave. We study this phenomenon for two PDE. The first SSE, for the intermediate long wave equation, is constructed to approximate general smooth Klaus-Shaw initial data. We first conduct a heuristic WKB approximation to determine the approximate scattering data and then rigorously study the inverse scattering problem using the methods of Lax and Levermore. We show the initial condition is recovered in the limit and the solution up until wave breaking approaches that of Invicid Burgers' equation in an L^2 sense. The second SSE is the sech^2 initial condition for the Korteweg-de Vries equation. Inverse scattering is done via a Reimann-Hilbert problem and the method of nonlinear steepest descent is employed. This project is joint work with K. Schmidt (University of Central Florida) and R. Buckingham (University of Cincinnati).
March 9, 2026, 4:00–5:00 pm, zoom
Speaker: Alessandro Arsie (The University of Toledo)
Title: An introduction to Dirac geometry and reduction schemes for concurrent Dirac structures.
Abstract: I will provide first a gentle introduction to Dirac geometry, which is a way to unify pre-symplectic and Poisson geometry, as well as turning possibly singular Poisson structures into a perfectly smooth object.
After this, I will consider a particular situation of transferring Dirac structures which is the following: given an embedded submanifold X of a Dirac manifold (M, L_M) and given p: X -> Y a smooth surjective submersion, we want to derive the minimal set of conditions to transfer the Dirac structure L_M on M to a Dirac structure L_Y on Y. These conditions are however not compatible with concurrence, which is a generalization for Dirac structures of the notion of commuting Poisson pairs.
Then I will characterize a geometric structure, more precisely a vector bundle E\subset TM|_X that is a \emph{witness} for concurrence: it allows to transfer weakly concurrent Dirac structures on M to weakly concurrent Dirac structures on Y. We show that the Marsden-Ratiu reduction in Poisson geometry is exactly a special case of this construction. Furthermore, in the presence of a Hamiltonian action of a Lie group G on L_M, there is a natural candidate for a witness E.
The main results carry over to the case of complex Dirac structures. This allows us to give an extension of the bi-Hamiltonian reduction of Casati, Magri e Pedroni in terms of our framework and provide a (conjectural) interpretation of it in terms of complex Dirac structures.
This talk is based on a joint work with Dan Aguero, Pedro Frejlich and Igor Mencattini.
March 16, 2026, 4:00–5:00 pm, East Hall 1866
Speaker: Deniz Bilman (University of Cincinnati)
Title: Extreme Superposition: Rogue Waves of Infinite Order, Universality, and Anomalous Temporal Decay
Abstract: Focusing nonlinear Schrödinger equation serves as a universal model for the amplitude of a wave packet in a general one-dimensional weakly-nonlinear and strongly-dispersive setting that includes water waves and nonlinear optics as special cases. Rogue waves of infinite order are a novel family of solutions of the focusing nonlinear Schrödinger equation that emerge universally in a particular asymptotic regime involving a large-amplitude and near-field limit of a broad class of solutions of the same equation. In this talk, we will present several recent results on the emergence of these special solutions along with their interesting asymptotic and exact properties. Notably, these solutions exhibit anomalously slow temporal decay and are connected to the third Painlevé equation. Finally, we will extend the emergence of rogue waves of infinite order to the first several flows of the AKNS hierarchy—allowing for arbitrarily many simultaneous flows—and report on recent work regarding their space-time asymptotic behavior under a general flow from the hierarchy.
March 30, 2026, 4:00–5:00 pm, East Hall 1866
Speaker: Robert Jenkins (University of Central Florida)
Title: Mathematical models of soliton gas
Abstract: In this talk I will describe the idea of a soliton gas, which seeks to describe large-amplitude coherent structures as a dense ensemble of interacting solitons. We will discuss the original motivation of Zakharov; some more recent results extending his ideas to more robust settings; finally, we will discuss our recent attempts to give the theory a more rigorous mathematical foundation and to connect the two main approaches to modeling soliton gas.
April 6, 2026, 4:00–5:00 pm, zoom
Speaker: Benjamin Harrop-Griffiths (Georgetown University)
Title: Some recent progress on the intermediate long wave equation
Abstract: The intermediate long wave equation (ILW) is a model for internal waves in a stratified fluid. The ILW is not just a completely integrable PDE - it also provides a bridge between two other integrable PDEs: the Korteweg-de Vries and Benjamin-Ono equations. In this talk, I will present some recent results on the ILW. In particular, I will discuss a priori estimates in Sobolev spaces and the regularity gain of the solution map in the shallow water limit. This is joint work with Rowan Killip and Monica Vișan and with Andreia Chapouto, Guopeng Li, and Tadahiro Oh.
April 20, 2026, 4:00–5:00 pm, East Hall 1866
Speaker: Robert Buckhingham (University of Cincinnati)
Title: Large-Degree Asymptotics of Rational Painleve-V Functions
Abstract: The Painleve-V equation has two families of rational solutions, one built from generalized Umemura polynomials and one built from generalized Laguerre polynomials. These solutions have drawn interest because they arise in a variety applications and because their zeros and poles exhibit remarkable geometric structures. We formulate Riemann-Hilbert problems for both families and obtain large-degree asymptotic results using nonlinear steepest-descent analysis. Results for the generalized Umemura solutions are joint with Matthew Satter of the University of Michigan and the results for the generalized Laguerre solutions are joint with Trevor Johnson of the University of Cincinnati.
Fall 2025
September 9, 2025, 9:00–10:00 am, zoom
Speaker: Yuancheng Xie (Shenzhen MSU-BIT University)
Title: Pfaffians as τ -functions of the BKP hierarchy: a constructive parametrization of complex pure spinors de E. Cartan
Abstract: It is well known that τ -functions of KP hierarchy are parameterized by points in Sato’s Universal Grassmannian manifold (UGM). These τ -functions have Schur expansions with coefficients satisfying Plücker relations. In this talk we will show that all τ -functions of BKP hierarchy can be written as Pfaffians of skew-symmetric matrices. These τ -functions are parameterized by points in the universal orthogonal Grassmannian manifold (UOGM). They have natural Schur-Q expansions with coefficients satisfying Cartan-Plücker relations. As a byproduct this parameterization gives a constructive description for complex pure spinors de E. Cartan. As an application, we reprove a theorem due to A. Alexandrov which states that τ -functions of KdV satisfy BKP up to rescaling of the time parameters by 2. We prove this by showing that the KdV hierarchy can be viewed as 4-reduction of the BKP hierarchy. This interpretation gives complete characterization for the KdV orbits nside the BKP hierarchy. This talk is based on preprint arXiv:2210.03307.
September 22, 2025, 4:00–5:00 pm, East Hall 1866
Speaker: Yelena Mandelshtam (University of Michigan)
Title: KP solitons from algebraic curves and the positive Grassmannian
Abstract: The Kadomtsev–Petviashvili (KP) equation is an important nonlinear PDE in the theory of integrable systems, with rich families of solutions arising both from algebraic geometry and from combinatorics. On one hand, Krichever showed how to build solutions from algebraic curves using Riemann theta functions. On the other, Kodama and Williams connected soliton solutions to the geometry of the positive Grassmannian. In this talk I will describe recent and ongoing work with various collaborators, where we study what happens when algebraic curves degenerate tropically. In this limit, theta-function solutions collapse to soliton solutions, and we can track how the geometry of the tropical curve manifests in the combinatorial structure of the soliton. This provides a new bridge between the algebro-geometric and combinatorial approaches to KP solutions.
September 30, 2025, 9:00–10:00 am, zoom
Speaker: Xi Chen (University of Basel)
Title: Gérard-type explicit formulas and their applications
Abstract: This talk will focus on the explicit formulas initially introduced by Patrick Gérard (2022), a powerful tool that provides more direct access to analyzing the solutions of integrable equations such as the Benjamin-Ono equation and the Calogero-Moser DNLS equation. We will also discuss three applications: the analysis of the zero dispersion limit, the characterization of long-time behavior, and the construction of new numerical schemes.
October 7, 2025, 9:00–10:00 am, zoom
Speaker: Jiaqi Liu (University of Chinese Academy of Sciences)
Title: On perturbation of completely integrable PDEs
Abstract: We revisit the perturbative theory of infinite-dimensional integrable systems developed
by P. Deift and X. Zhou, aiming to provide new and simpler proofs of some key
L∞ bounds and Lᵖ a priori estimates. Our proofs emphasize a further step towards
understanding focusing problems and extending the applicability to other integrable
models. As a concrete application, we examine the perturbation of the one-dimensional
defocusing cubic nonlinear Schrödinger equation and modified KdV equations.
October 21, 2025, 9:00–10:00 am, zoom
Speaker: Anton Dzhamay (BIMSA)
Title: On the geometric approach to the Painlevé equivalence problem
Abstract: We show how the techniques from the Okamoto-Sakai geometric theory of Painlevé equations can be used to solve the Painlevé equivalence, i.e., how to recognize an equation as a Painlevé equation and find an explicit change of variables transforming it into some canonical form. We illustrate the geometric approach by considering two examples recently obtained by M. van der Put and J. Top in their study of a certain ansatz of isomonodromic deformations of linear ODEs. We provide explicit coordinate transformations identifying these examples with standard form of some Painlevé equations and also explicitly identify their Hamiltonians.
November 3, 2025, 4:00–5:00 pm, East Hall 1866
Speaker: Shi-Zhuo Looi (Caltech)
Title: Late-time tails and nonlinear Price's law for semilinear wave equations in 3-D
Abstract: I will present sharp late-time pointwise asymptotics for semilinear wave equations with power nonlinearities on stationary, asymptotically flat spacetimes (including black hole exteriors). Under standard spectral and local energy decay hypotheses for perturbations of black-hole backgrounds, we show a clean dichotomy: cubic nonlinearities generate a nonlinear t^{-2} tail with an explicit coefficient, while for powers p \ge 4 the linear Price's law t^{-3} decay holds with a modified coefficient; in both regimes we identify the leading term throughout the forward causal domain via a blend of radiation-field methods and low-energy resolvent analysis. Joint work with Haoren Xiong.
November 11, 2025, 9:00–10:00 am, zoom
Speaker: Alex Little (ENS de Lyon)
Title: The partition function of β-ensembles with complex potentials
Abstract: The asymptotic behaviour of the partition function is one of the central questions of statistical mechanics. In our work we consider this problem when the external potential is complex valued and for a particular statistical-mechanical model, a β-ensemble. We prove a full 1/N expansion of the logarithm of the partition function, the so-called free energy. Our method can be regarded as an infinite dimensional version of the method of steepest descent for contour integrals. This is joint work with A. Guionnet and K. Kozlowski.
November 17, 2025, 4:00–5:00 pm, East Hall 1866
Speaker: Antonios Zitridis (University of Michigan)
Title: From entropic propagation of chaos to concentration bounds for stochastic particle systems
Abstract: We shall discuss about weakly interacting stochastic particle systems with possibly singular pairwise interactions. In this setting, we observe a connection between entropic propagation of chaos (proved by Jabin and Wang, 2018) and exponential concentration bounds for the empirical measure of the system. In particular, we will show how to establish a variational upper bound for the probability of a certain rare event, and then use this upper bound to show that ''controlled" entropic propagation of chaos implies an exponential concentration bound for the empirical measure.
December 1, 2025, 4:00–5:00 pm, East Hall 1866
Speaker: Andres Contreras Hip (University of Chicago)
Title: Gaussian fluctuations for the open one-dimensional KPZ equation
Abstract: In this talk we consider the open one-dimensional KPZ equation on the interval $[0,L]$ with Neumann boundary conditions. For $L \sim t^{\alpha}$ and stationary initial conditions, we obtain matching upper and lower bounds on the variance of the height function for $\alpha \in [0,\frac23]$ for different choices of the boundary parameters. Additionally, for fixed $L$ and an arbitrary probability measure as initial conditions, we show Gaussian fluctuations for the height function as $t\to \infty$. Joint work with Sayan Das and Antonios Zitridis.
December 8, 2025, 4:00–5:00 pm, East Hall 1866
Speaker: Andrei Prokhorov (University of Cincinnati)
Title: Connection formulas for the Heun equation from Painlevé theory
Abstract: Heun equation is the second order differential equation with 4 regular singularities and it plays important role in theoretical physics. Unlike the hypergeometric equation, which has 3 regular singularities, the connection formulas for Heun equation don't have expressions in terms of elementary functions. Recently they were written in terms of semiclassical conformal blocks by Bonelli-Iossa-Lichtig-Tanzini. We derive these formulas using the interplay between Heun equations and Painlevé equations. This computation in particular provides the expression for the semiclassical conformal blocks within the Painlevé theory. This is the joint work with Harini Desiraju, Promit Ghosal, and Oleg Lisovyy.
Winter 2025
March 10, 2025, 3:00–4:00pm, East Hall 3096
Speaker: Brian Hall (University of Notre Dame)
Title: Roots of polynomials under differential flows, with connections to random matrix theory
Abstract: I will discuss how the roots of polynomials evolve under differential flows, focusing on two main examples: heat flow and repeated differentiation. In the case of real roots, the situation is well understood and the evolution of the roots is described by constructions from random matrix theory. In the case of complex roots, I will present a general PDE-based conjecture, together with a random matrix interpretation. Finally, I will describe recent rigorous results for random polynomials.
The talk will be self-contained and have lots of pictures and animations.
March 17, 2025, 4:00–5:00pm, zoom
Speaker: Samir Donmazov (University of Kentucky)
Title: Long-Time Asymptotics of Solutions to the Kadomtsev-Petviashvili I Equation
Abstract: We establish the long-time asymptotics for solutions of the Kadomtsev-Petviashvili I (KP I) equation $$ (u_t+6uu_x+u_{xxx})_x = 3 u_{yy} $$ with small initial data, using the inverse scattering transform (IST) formalism developed by Zhou. Within this framework, the inverse problem for the KP I equation is formulated as a nonlocal Riemann-Hilbert problem (RHP) in two dimensions. As part of the asymptotic analysis, we also determine the long-time behavior of the solution to the nonlocal RHP, along with its $x$-derivative.
March 31, 2025, 4:00–5:00pm, East Hall B745
Speaker: Alexander Moll (Reed College)
Title: Fractional Brownian motions and Kerov's CLT
Abstract: Nonlinear functionals of Gaussian fields are ubiquitous in probability theory and PDEs. We introduce a family of random curves in the plane which encode the random values of certain nonlinear functionals of fractional Brownian motions on a circle with Hurst index s - 1/2. For a special choice of Cameron-Martin shift, the low variance limit of the fractional Brownian motion induces a LLN and CLT for the associated random curves that is nearly identical to the global behavior of Plancherel measures on large Young diagrams. The limit shape is independent of s and is that of Vershik-Kerov-Logan-Shepp. The global Gaussian fluctuations depend on s and coincide with the process in Kerov's CLT for s = -1/2. We give a dynamical explanation of this relationship using results of Eliashberg and Dubrovin. This is work in progress with Robert Chang (Rhodes College).
Fall 2024
October 21st 4-5pm EDT - Cade Ballew (University of Washington)
Title: Numerical solutions of Riemann--Hilbert problems on disjoint intervals
Abstract: We present a general approach to numerically compute the solutions of Riemann--Hilbert problems with jump conditions supported on disjoint intervals. Applied to the Fokas--Its--Kitaev Riemann--Hilbert problem, this enables the computation of orthogonal polynomials on multiple intervals, requiring only O(N) arithmetic operations to compute the first N recurrence coefficients. Such recurrence coefficients describe the flow of a semi-infinite Toda lattice, and expansions in these orthogonal polynomials yield a novel iterative method for solving indefinite linear systems and computing matrix functions, further yielding a fast algorithm for computing the solutions of Sylvester matrix equations. Other Riemann--Hilbert problems of this form yield finite-genus and soliton gas solutions of the Korteweg--de Vries equation. In particular, we compute large-genus solutions to simulate dispersive quantization and evaluate soliton gas solutions before asymptotic estimates are valid.
October 28th 4-5pm EDT - Nathan Hayford (KTH Royal Institute of Technology)
Title: Critical phenomena in the 2-matrix model: the Ising model coupled to gravity
Abstract: The unitary invariant ensembles of random matrix theory (collectively referred to as the `1-matrix model’) are one of the central objects of study in the theory of random matrices. Upon tuning the parameters of this model, one can realize certain `higher-order' eigenvalue correlations at the endpoints of the density of eigenvalues. In the 1-matrix model, these higher-order correlation kernels can be written in terms of special solutions of the Painlevé I and II hierarchies. We refer to such special tunings as critical phenomena.
The 2-matrix model is an extension of the 1-matrix model, which came to be well-studied in part because it admits a much richer class of critical phenomena. In this talk, I will survey some of the conjectures regarding these critical phenomena from the physics literature, and discuss some of the physical implications of these results. In particular, I will discuss some forthcoming work (joint with Maurice Duits and Seung-Yeop Lee) regarding a special critical phenomenon in the 2-matrix model, which has implications in the theory of the Ising minimal model coupled to topological gravity.
November 4th 4-5pm EDT - Patrick Sprenger (University of California, Merced)
Title: The Riemann problem for a discrete conservation law
Abstract: The hydrodynamics of a system of conservation laws can often be understood by studying solutions to a Riemann problem, i.e., the evolution of step initial data in a hyperbolic system. When dispersion compensates for the large gradients induced by this initial data, wave-breaking is often resolved by a dispersive shock wave (DSW). An active area of research is the investigation of quantitative features of DSWs in continuum models arising in physical applied mathematics. This talk leverages modern techniques to investigate solutions of the Riemann problem for a semi-discrete conservation law. The semi-discrete model is obtained by applying a first-order centered difference scheme to the spatial derivative of the Hopf equation. Solutions to the Riemann problem reveal a surprisingly elaborate set of solutions to this example system. In addition to discrete analogs of well-known dispersive hydrodynamic solutions—rarefaction waves (RWs) and DSWs—additional unsteady solution families and finite-time blow-up are observed and characterized. We will also compare the dynamics of the Riemann problem to an integrable discretization of the spatial derivative.
November 18th 4-5pm EST - Seung-Yeop Lee (University of South Florida)
Title: Planar orthogonal polynomials with non-Hele-Shaw type polynomial potentials
Abstract: Planar orthogonal polynomials in the double scaling limit have been much studied for their connection to Coulomb gas system in two dimensions. Most exact results have been known either for radially symmetric potential or for so-called Hele-Shaw potential, where the limiting density of the Coulomb gas is uniform over its support. When the potential is not Hele-Shaw type nor radially symmetric, we expect to observe a new type of singular behaviors. Unfortunately, in such cases, there is no known multiple orthogonality that we can use for asymptotic analysis of the planar polynomials.
In this talk, we will propose a matrix Riemann-Hilbert problem for some polynomial potential that is not radially symmetric and not Hele-Shaw type. More explicitly we will consider the case when the Laplacian of the potential is |z|^2. This work is a preliminary report of the work by Abril Arenas and by Seong-Mi Seo.
November 25th 4-5pm EST - Michel Alexis (Hausdorff Center for Mathematics)
Title: How to represent a function in a quantum computer?
Abstract: Quantum Signal Processing (QSP) is an algorithmic process by which one represents a signal $f:[0,1] \to (-1,1)$ as the upper left entry of a product of SU(2) matrices parametrized by the input variable $x \in [0,1]$ and some "phase factors'' $\{\psi_k\}_{k \geq 0}$ depending on $f$. We show that, after a change of variables, QSP is actually the SU(2)-valued nonlinear Fourier transform, and the phase factors correspond to the nonlinear Fourier coefficients. By exploiting a nonlinear Plancherel identity and using some basic spectral theory, we show that QSP can be done for any signal f satisfying the log integrability condition
\int\limits_{0} ^1 \log (1-f(x)^2) \frac{dx}{\sqrt{1-x^2}} > - \infty .
December 2nd 4-5pm EST - Ahmad Barhoumi (KTH Royal Institute of Technology)
Title: Non-Hermitian orthogonality in the q^(Volume) tiling model
Abstract: Consider a hexagon overlayed on a regular triangular grid, where the equilateral triangles have sidelength 1. A "lozenge" is a pair of adjacent triangles, and there are three types of lozenges that can be built on this grid. Using these lozenges, one can tile the entire hexagon. Lozenge tilings of a regular hexagon are in bijection with boxed plane partitions (i.e. stacks of boxes in the back of a cubic room) and can therefore be assigned a volume; a fact that is best illustrated by staring at a picture of one such tiling. The q^(Volume) tiling model is a measure on the space of tilings of the hexagon which assigns to each tiling a probability proportional to q^(Volume), where q is a real parameter. In this talk, I will recall the model and basic result about it and propose an approach to studying its statistical properties as the size of the hexagon grows by analyzing a related family of non-Hermitian orthogonal polynomials. The talk is based on ongoing joint work with Maurice Duits.