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Organizing Committee
Brown University
Seoul National University and University of Massachusetts Amherst
University of the Aegean
Northeastern University
Abstract
The palette of coherent structures in nonlinear media is very rich extending from the classic 1D ones like pulses, fronts, kinks, breathers, (dark/bright) solitons, to higher-dimensional ones like vortices, vortex rings and knots, spiral waves and more exotic ones like skyrmions and monopoles. These structures are highly interesting in their own right, but also play a crucial role as building blocks towards understanding more complicated and realistic features of the full underlying systems.
The methodologies of studying this field vary from techniques taken from mathematical analysis and differential equations to numerical analytical and machine learning techniques, while experiments always play a crucial role in touching base with respect to physical reality. This conference aims to bring together people both from the analytical and the computational worlds, along with experimental practitioners, to discuss the state-of-the-art and emergent challenges of the field of nonlinear waves and coherent structures. It will accordingly seek to establish a mutually beneficial dialogue which could provide valuable insights in different directions, setting the stage towards future investigations.
The methodologies of studying this field vary from techniques taken from mathematical analysis and differential equations to numerical analytical and machine learning techniques, while experiments always play a crucial role in touching base with respect to physical reality. This conference aims to bring together people both from the analytical and the computational worlds, along with experimental practitioners, to discuss the state-of-the-art and emergent challenges of the field of nonlinear waves and coherent structures. It will accordingly seek to establish a mutually beneficial dialogue which could provide valuable insights in different directions, setting the stage towards future investigations.
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Workshop Schedule
Monday, April 27, 2026
8:50 - 9:00 AM EDT
Welcome
11th Floor Lecture Hall
Brendan Hassett, ICERM/Brown University
9:00 - 9:45 AM EDT
Snaking of localized time-dependent oscillations
11th Floor Lecture Hall
Speaker
Edgar Knobloch, UC Berkeley
Session Chair
Panayotis Kevrekidis, Seoul National University and University of Massachusetts Amherst
Abstract
In this talk I will describe recent work on the snaking of spatially localized oscillations
in two systems of interest, the cubic-quintic complex Swift-Hohenberg equation and a
three-species reaction-diffusion system (the Purwins system) admitting a primary wave bifurcation, i.e. a Hopf bifurcation with a finite wavenumber. On a one-dimensional periodic domain this bifurcation gives rise simultaneously to two solution branches, standing and traveling waves of uniform amplitude, and we focus on the case where both bifurcate subcritically. We study in detail the properties, including stability, of spatially localized states (traveling pulses and spatial localized standing waves) originating in secondary bifurcations from these primary states. Tertiary bifurcations leading to drifting localized oscillations are also studied. These results are extended to wall-attached structures in a disk. These are found to mimic qualitatively the behavior in one spatial dimension, modified for some parameter values by the excitation of bulk modes of the disk. Our results are complemented with direct numerical simulations and compared with related results for breathers.
This work is joint work with S. Modai, H. Uecker, N. Verschueren and A. Yochelis.
10:00 - 10:30 AM EDT
Coffee Break
11th Floor Collaborative Space
10:30 - 11:15 AM EDT
Modulation theory for a continuum dispersive approximation of FPU dynamics
11th Floor Lecture Hall
Speaker
Anna Vainchtein, University of Pittsburgh
Session Chair
Panayotis Kevrekidis, Seoul National University and University of Massachusetts Amherst
Abstract
We consider a dispersive quasicontinuum approximation of the Fermi-Pasta-Ulam problem governed by the modified regularized Boussinesq equation. We focus on the case of general cubic nonlinearity, which allows us to obtain explicit periodic traveling wave solutions and their solitary-wave and kink limits. We derive Whitham modulation equations and analyze their convexity, analytically in the solitary-wave and harmonic limits and numerically in the general case. In particular, we identify the parameter regions where the modulation system loses strict hyperbolicity, which leads to modulational instability of periodic traveling waves. The onset of modulational instability is verified by numerical computations of the linear spectra and initial value problems that also reveal additional short-wave instabilities.
Joint work with Mark Hoefer (CU Boulder).
11:30 AM - 12:15 PM EDT
Quantized soliton motion in Nonlinear Photonic Thouless Pumps
Virtual
Virtual Speaker
Mikael Rechtsman, The Pennsylvania State University
Session Chair
Panayotis Kevrekidis, Seoul National University and University of Massachusetts Amherst
Abstract
I will present my group’s recent experimental work on the fractional pumping of solitons in nonlinear photonic Thouless pumps, using waveguide arrays. Specifically, I will show that the displacement (in unit cells) of solitons in Thouless pumps is strictly quantized to the Chern number of the band from which the soliton bifurcates in the low power regime; whereas in the intermediate power regime, nonlinear bifurcations lead to fractional quantization of soliton motion. This fractional quantization can be predicted from multi-band Wannier functions associated with the states of the pump.
12:30 - 2:00 PM EDT
Lunch/Free Time
2:00 - 2:45 PM EDT
TBA
11th Floor Lecture Hall
Speaker
Theodore Kolokolnikov, Dalhousie University
Session Chair
Vassilis Koukouloyannis, University of the Aegean
3:00 - 4:15 PM EDT
4:15 - 5:00 PM EDT
Generation of deterministic and directional rogue waves in a basin
11th Floor Lecture Hall
Speaker
Amin Chabchoub, University of Sydney
Session Chair
Vassilis Koukouloyannis, University of the Aegean
Abstract
Rogue waves pose a significant threat to marine vessels and offshore infrastructure, making a clear understanding of their dynamics and kinematics essential. While numerical and experimental modeling plays a crucial role in this effort, an ongoing debate within the research community concerns the relative importance of nonlinearity and unstable wave groups in the formation of realistic, directional rogue waves. This talk addresses this issue by highlighting the pivotal role of weakly nonlinear wave theory in the generation and control of deterministic and directional rogue waves, both in the open ocean and in controlled water-wave basin experiments.
Tuesday, April 28, 2026
9:00 - 9:45 AM EDT
NLS models with intensity-dependent dispersion
11th Floor Lecture Hall
Speaker
Dmitry Pelinovsky, McMaster University
Session Chair
Zhiyuan Zhang, Northeastern University
Abstract
We study standing periodic waves modeled by the nonlinear Schrodinger equation with the intensity-dependent dispersion coefficient. Spatial periodic profiles are smooth if the frequency of the standing waves is below the limiting frequency, for which the profiles become peaked (piecewise continuously differentiable with a finite jump of the first derivative). We prove that there exist two families of the periodic waves with smooth profiles separated by a homoclinic orbit and the period function (the energy-to-period mapping) is monotonically increasing for the family inside the homoclinic orbit and decreasing for the family outside the homoclinic orbit. This property allows us to derive a sharp criterion for the energetic stability of such standing periodic waves under time evolution if the perturbations are periodic with the same period.
10:00 - 10:45 AM EDT
Breathers in nonlinear wave equations and "hard" implicit function theorems.
11th Floor Lecture Hall
Speaker
Eugene Wayne, Boston University
Session Chair
Zhiyuan Zhang, Northeastern University
Abstract
Breathers are temporally periodic, spatially localized, solutions of nonlinear wave equations or other, spatially extended, infinite dimensional dynamical systems. They are rare, because localized oscillations in such systems tend to be destroyed by resonances with the dispersive modes in the system. While breathers have been shown to exist some nonlinear wave equations with spatially periodic coefficients, these examples require rather special conditions on the coefficients. I'll explain why Nash-Moser, or "hard", implicit function theorems are a natural tool to try to expand the class of equations for which breathers exist.
11:00 - 11:15 AM EDT
Coffee Break
11th Floor Collaborative Space
11:15 - 11:30 AM EDT
Thermalization of the discrete nonlinear Schrodinger equation: Theory, computation and experiments
Contributed Talks - 11th Floor Lecture Hall
Ziad Musslimani, Florida State University
Abstract
I will present a comprehensive study related to the connection between thermalization of cubic nonlinear lattices with nearest-neighbor coupling and the structure of the mixing tensor that arises due to the presence of nonlinearities. The approach is based on rewriting the underlying lattice system as a nonlinear evolution equation governing the dynamics of the modal amplitudes (or projection coefficients). In this formulation, the linear coupling become diagonalizable, whereas all cubic nonlinear terms transform into a combinatorial sum over a product of three modal amplitudes weighted by a fourth order mixing tensor. The exact structure of several mixing tensors (corresponding to different types of cubic nonlinearities) is found, and their symmetry properties are connected with thermalization or lack thereof. Furthermore, through direct numerical simulations, it is found that the modal occupancies of lattices preserving these tensorial symmetries approach a Rayleigh-Jeans distribution at thermal equilibrium. In addition, few examples that indicate that cubic lattices with broken tensorial symmetries end up not equilibrating to a Rayleigh-Jeans distribution are presented. Finally, an inverse approach to the study of thermalization of cubic nonlinear lattices is developed. The idea is to establish a trade-off between the type of nonlinearities in local base and their respective interactions in supermode base. With this at hand, we were able to
identify a large class of nonlinear lattices that are embedded in the modal space and admit a simple form that can be used to shed more light on the role that localization of the supermodes plays in thermalization processes.
11:35 - 11:50 AM EDT
Nonlinear waves in two spatial dimensions: modulation theory, dispersive shocks and applications
Contributed Talk - 11th Floor Lecture Hall
Gino Biondini, State University of New York at Buffalo
Abstract
The talk will present an overview of recent results on the development of Whitham modulation theory for two-dimensional nonlinear evolution equations, focusing primarily on the Kadomtsev-Petviashvili (KP) equation, as well as the description of various dynamical problems such as transverse stability of periodic traveling wave solutions, oblique interactions between line solitons and mean flow, the formation of two-dimensional dispersive shock waves, and steady shallow water flow past an obstacle.
11:55 AM - 12:10 PM EDT
Global Attractors for a class of bore models
Contributed Talk - 11th Floor Lecture Hall
Jared Bronski, University of Illinois
Abstract
There has been recent progress using energy arguments to prove that certain dispersive shocks -- for instance the KdV Burgers traveling waves -- are global attractors. The proof involves some variations of classical mathematical physics techniques for counting the number of bound states together with (at least for certain ranges of the dispersion parameter) some rigorous computations based on the Sturm oscillation theorem.
12:15 - 1:45 PM EDT
Lunch/Free Time
1:45 - 2:30 PM EDT
Topological solitons and their role in the long-term dynamics of classical field theories
11th Floor Lecture Hall
Speaker
Wilhelm Schlag, Yale University
Session Chair
Justin Holmer, Brown University
Abstract
Following the 2004 Cambridge book by Manton and Sutcliffe Topological Solitons, we recall three classical field theories via their Lagrangians: i) scalar fields on the line associated with kinks (the topological invariant is the charge) ii) wave maps in the energy critical regime associated with harmonic maps (the invariant is the degree) iii) Ginzburg-Landau (non-magnetic or non-gauged) and abelian Yang-Mills-Higgs models (magnetic or gauged) associated with vortices (the invariant is the degree). The gradient flow associated with the underlying Hamiltonian leads to dissipative dynamics in the form of a heat equation, while the most common conservative time evolutions are the Schrödinger flow (with Galilei symmetry), respectively the wave or Klein-Gordon flow (with Lorentz symmetry). In each of these infinite-dynamical systems we would like to describe or even classify the long-term behavior of trajectories. This is a deeply challenging problem as a multitude of phenomena might arise (breathers and wobbling kinks in the sine-Gordon equation, multi-kink/antikink solutions in the phi-4 model, bubbling in the harmonic map heat flow, vortex splitting and vortex collisions in Ginzburg-Landau). As stationary solutions, solitons and their moduli space play a fundamental role in the complicated dynamics. A starting point here is the question of asymptotic stability of these equilibria. While the past 20 years have seen dramatic advances, we are still far from a complete understanding. We will survey some of the work in this direction - both past and ongoing - which combines techniques from elliptic PDEs, the spectral and scattering theory of linear differential equations, harmonic analysis and linear dispersive estimates, and nonlinear dispersive equations (space-time resonances, normal forms, vector fields, Fermi Golden Rule).
2:45 - 3:00 PM EDT
On kink solutions for dispersive-diffusive models
11th Floor Lecture Hall
Speaker
Atanas Stefanov, University of Alabama - Birmingham
Session Chair
Justin Holmer, Brown University
Abstract
We consider traveling kinks for two dispersive-diffusive models - KdV-Burger and the viscous Boussinesq. Under very general condition, we show asymptotic stability of such kinks. The Boussinesq result uses fairly straightforward energy estimates (and a bit of spectral theory), while for the KdV-Burger, we built upon recent works about attractivity and we bootstrap the time decay rates.
3:05 - 3:20 PM EDT
On the proximity between solutions to certain integrable systems and their non- integrable generalizations
11th Floor Lecture Hall
Speaker
Dionyssis Mantzavinos, University of Kansas
Session Chair
Justin Holmer, Brown University
Abstract
The question of persistence of dynamics between integrable systems and their non-integrable counterparts is a central one in terms of both theory and applications. In this talk, we explore this direction in the context of (1) the (continuum model) cubic nonlinear Schrödinger equation and (2) the (discrete model) Ablowitz-Ladik equation, both of which are prime examples of completely integrable systems. Specifically, we discuss the proximity of solutions between these two models and a broad class of non-integrable generalizations in the framework of the associated initial value problem on the whole line. We consider the standard case of initial data that decay to zero at infinity, as well as the more intriguing case of nonzero boundary conditions at infinity which induces the phenomenon of modulational instability in focusing media. The talk is based on joint works with D.Hennig, N. Karachalios, J. Cuevas-Maraver, D. Mitsotakis, and I. Stratis.
3:25 - 3:40 PM EDT
Stability of dispersive shock in KdV Burgers’ equation
11th Floor Lecture Hall
Yannan Shen, University of Kansas
Abstract
We will talk about the stability of viscous-dispersive shock profile with infinite oscillations of the Korteweg de Vries Burgers (KdVB) equation. First, we establish detail structures of the shock wave, including the rate at which the local extrema converge to the left end state towards the left far field. Then, by exploiting the structural properties of the shock, we show the L2 contraction property of the shock profile under arbitrarily large perturbations, up to a time-dependent shift. This result implies both time-asymptotic stability and uniform stability with respect to the viscosity and dispersion coefficients. This uniformity yields zero viscosity-dispersion limits.
3:45 - 4:00 PM EDT
Coffee Break
11th Floor Collaborative Space
4:00 - 4:45 PM EDT
TBA
11th Floor Lecture Hall
Speaker
Susanna Haziot, Princeton Univesity
Session Chair
Justin Holmer, Brown University
Wednesday, April 29, 2026
9:00 - 9:45 AM EDT
Nonlinear waves in flexible mechanical metamaterials
11th Floor Lecture Hall
Speaker
Katia Bertoldi, Harvard University
Session Chair
Vassilis Koukouloyannis, University of the Aegean
Abstract
Flexible mechanical metamaterials are compliant structures engineered to achieve unique properties via the large deformation of their components. While their static character has been studied extensively, the study of their dynamic properties is still at an early stage, especially in the nonlinear regime induced by their high deformability. Nevertheless, recent studies show that these systems provide new opportunities for the control of large amplitude elastic waves. In this talk, I will present recent results on the propagation of nonlinear waves in flexible elastic metamaterials.
10:00 - 10:45 AM EDT
Topological photonics: A mathematical perspective
11th Floor Lecture Hall
Speaker
Alejandro Aceves, Southern Methodist University
Session Chair
Panayotis Kevrekidis, Seoul National University and University of Massachusetts Amherst
Abstract
In the field of light matter interactions, current technologies allow the design of optical media (photonic lattices, photonic crystals, metamaterials) so that novel states of light are created. As such, topological photonics refers to features of such states of light that are characterized by a topological (quantized) property, leading to for example robust propagation properties. This talk will introduce the audience to the field as well as highlight current developments.
10:55 - 11:00 AM EDT
Group Photo (Immediately After Talk)
11th Floor Lecture Hall
11:00 - 11:30 AM EDT
Coffee Break
11th Floor Collaborative Space
11:30 - 11:45 AM EDT
Unexpected Resonance Behavior for Nonlinear Waves in Fluids
Contributed Talks - 11th Floor Lecture Hall
Paul Milewski, Penn State University
Abstract
We discuss 2 problems where resonances yield unexpected results in fluids. One problem concerns whether mode 2 solitary waves exist in stratified flows (such as the ocean). Based on physical intuition, this type of solitary wave is not expected to exist because of the dissipative effects of resonant energy radiation. However, we show that such waves do exist at particular (discrete) amplitudes. A second problem concerns surface gravity waves in a cylindrical container. This is a classic problem, and conventional wisdom is that resonances between 3 waves (triad resonances) are impossible, perhaps because they do not exist in unbounded problems and in rectangular domains. We give a complete characterization of the generic character of such resonances in arbitrary cross-sectional cylinders, given the spectrum of the Laplacian on its cross-section. This demonstrates how boundaries can alter fundamental nonlinear wave resonance properties and how non-sinusoidal eigenfunctions play a critical role.
11:50 AM - 12:05 PM EDT
Swinging waves in the Ablowitz-Ladik equations
Contributed Talk - 11th Floor Lecture Hall
Igor Barashenkov, University of Cape Town
Abstract
We construct a novel family of exact cnoidal wave and soliton solutions of the focusing and defocusing Ablowitz-Ladik equations. Unlike cnoidal waves that were obtained by earlier authors, the phase variable of the new solutions exhibits a nonlinear dependence on time and site number; the wave ``swings". Our approach hinges on the existence of a two-point map governing the absolute value of the complex field; this map gives rise to standing waves centred arbitrarily relative to the lattice sites. Having derived stationary solutions, we use these as a basis for constructing waves with nonzero velocity. The localised members of the new family comprise dark solitons with the nontrivial asymptotic behaviour. We identify periodic and quasiperiodic patterns and establish an explicit quantisation rule for the velocity of the wave circulating in a closed loop of $N$ sites.
12:10 - 12:25 PM EDT
Variational approach to Klein-Gordon oscillons
Contributed Talk - 11th Floor Lecture Hall
Nora Alexeeva, University of Cape Town
Abstract
We aim to obtain a variational description of the Klein-Gordon oscillon reproducing its energy-frequency dependence outside the small-amplitude limit. The variational method employing the amplitude and width as collective coordinates leads to a dynamical system with unstable periodic orbits that blow up when perturbed. We propose a multiscale variational approach free from the blowup singularities. An essential feature of the proposed trial function is the inclusion of the third collective variable: a correction for the nonuniform phase growth. In addition to determining the parameters of the oscillon, the new approach detects the onset of its instability. A further refinement of our method uses the full anharmonic oscillation instead of substituting it with a truncated Fourier expansion. Finally, the variational results are compared to standing waves obtained by the numerical solution of a boundary-value problem on a two-dimensional periodic domain.
12:30 - 2:30 PM EDT
Lunch/Free Time
2:30 - 3:15 PM EDT
TBA
11th Floor Lecture Hall
Speaker
Sergej Flach, Institute for Basic Science
Session Chair
Vassilis Koukouloyannis, University of the Aegean
3:30 - 4:00 PM EDT
Coffee Break
11th Floor Collaborative Space
4:00 - 4:45 PM EDT
Rogue waves and the 2D water wave problem
11th Floor Lecture Hall
Speaker
Gigliola Staffilani, Massachusetts Institute of Technology
Session Chair
Panayotis Kevrekidis, Seoul National University and University of Massachusetts Amherst
Abstract
Rogue waves are extreme ocean events characterized by the sudden formation of anomalously large crests. This phenomenon remains an important subject of investigation in oceanography and mathematics. A central problem is to quantify the probability of their formation under random Gaussian sea initial data. We rigorously justify the exponential large-tail law probability for the formation of rogue waves of the pure gravity water wave equations in deep water, up to the optimal timescales allowed by deterministic well-posedness theory. The proof shows that rogue waves most likely arise through “dispersive focusing”, where phase synchronization produces constructive amplification of the water crest. The main difficulty in justifying this mechanism is propagating statistical information over such long timescales, which we overcome by combining normal forms and probabilistic methods. Unlike previous results, this novel approach does not require approximate solutions to be Gaussian.
This is joint work with M. Berti, R. Grande and A. Maspero
5:00 - 6:30 PM EDT
Reception
11th Floor Collaborative Space
Thursday, April 30, 2026
9:00 - 9:45 AM EDT
Nonlinear stability of periodic waves in Hamiltonian systems against localized perturbations
11th Floor Lecture Hall
Speaker
Björn de Rijk, Karlsruhe Institute of Technology
Session Chair
Zhiyuan Zhang, Northeastern University
Abstract
In Hamiltonian systems, periodic waves often correspond to coherent structures: recurrent, robust patterns that persist over time. Notable examples include water waves, periodic sequences of light pulses in nonlinear optical fibers, and soliton trains in Bose-Einstein condensates. To date, nonlinear stability results for periodic standing or traveling waves in Hamiltonian systems have primarily addressed co-periodic perturbations. A longstanding open problem concerns their stability with respect to localized perturbations: a natural setting in many physical applications. Standard stability arguments in Hamiltonian systems, characterizing solutions as constrained minimizers of an appropriate Lagrangian functional built from conserved quantities of the system, break down in this setting, since localized perturbations preclude coercivity on any finite-codimensional constraint space. In this talk, I propose an alternative framework that integrates variational arguments, Floquet-Bloch decomposition, and Duhamel-based estimates with a modulational ansatz. Our approach yields the first orbital stability results for periodic waves in key Hamiltonian models, such as the Korteweg-de Vries equation, with respect to L^2-localized perturbations. This is joint work with Emile Bukieda (Karlsruhe Institute of Technology).
10:00 - 10:15 AM EDT
Coffee Break
11th Floor Collaborative Space
10:15 - 11:00 AM EDT
Hollow desingularization of vortices
11th Floor Lecture Hall
Speaker
Kristoffer Varholm, University of Pittsburgh
Session Chair
Zhiyuan Zhang, Northeastern University
Abstract
It is well-known that there exist a number of steady solutions with point vortices to the Euler equations. Both configurations in the plane, and embedded in water waves. In recent years there has been a program to desingularize these steady solutions, by expanding the point vortices into hollow vortices. These are essentially spinning air bubbles. In this talk I will give an overview of this effort, including work in progress on hollow vortex rings.
11:15 AM - 12:00 PM EDT
Squared-eigenfunctions-based perturbation theory for dark solitons of the defocusing nonlinear Schrodinger equation
11th Floor Lecture Hall
Speaker
Barbara Prinari, Fulbright Foundation of Greece
Session Chair
Zhiyuan Zhang, Northeastern University
Abstract
In this talk, we will revisit the squared-eigenfunctions-based perturbation theory of the scalar defocusing nonlinear Schrodinger equation on a nonzero background, which we developed so that it can correctly predict the slow-time evolution of the dark soliton parameters, as well as the radiation shelf emerging on the sides of the soliton. Proof of the completeness of the squared eigenfunctions is provided. Our closure relation accounts for the singularities of the scattering data at the branch points of the continuous spectrum, which leads to the correct discrete eigenfunctions of the closure relation. Using the one-soliton closure relation and its correct discrete eigenmodes, the slow-time evolution equations of the soliton parameters are determined. Moreover, the first-order correction integral to the dark soliton is shown to contain a pole due to singularities of the scattering data at the branch points. Analysis of this first-order correction integral leads to predictions for the height, velocity and phase gradient of the shelves, as well as a formula for the slow time evolution of the soliton's phase, which in turn allows one to determine the slow-time dependence of the soliton center. We will also provide comparisons of our results with direct numerical simulations, and with earlier results.
12:15 - 1:45 PM EDT
Lunch/Free Time
1:45 - 2:30 PM EDT
Solitons in the 4th order NLS equation
11th Floor Lecture Hall
Speaker
Svetlana Roudenko, Florida International University
Session Chair
Justin Holmer, Brown University
Abstract
The 4th order (or bi-harmonic) NLS equation has recently been attracting attention of scientists as the experimental quartic solitons, aka light bullets, have been obtained. We discuss solutions to this equation, examining more carefully the ground states in one- and two-dimensional settings. We look at the soliton dynamics, including stability, branching and long-time behavior. This talk is based on joint works with Iryna Petrenko (FIU, Miami) and Christian Klein & Nikola Stoilov (IMB, Dijon).
2:45 - 3:30 PM EDT
Self-similar singular solutions for the nonlinear Schrödinger equation and the complex Ginzburg-Landau equation
11th Floor Lecture Hall
Speaker
Joel Dahne, University of Minnesota
Session Chair
Justin Holmer, Brown University
Abstract
In 2001, Plecháč and Sverak gave strong numerical evidence for the existence of branches of backwards self-similar singular solutions to the complex Ginzburg-Landau equation. We now present a rigorous proof of these branches' existence, which in particular includes the 3D cubic Schrödinger equation.
Our proof follows the same strategy as Plecháč and Sverak, which reduces the problem to proving the existence of a solution to a certain ODE with prescribed behaviour at zero and infinity. Near zero the solution is constructed using a rigorous numerical ODE solver and near infinity by carefully analysing the asymptotic expansion. These two solutions are then glued together to form the full solution.
3:45 - 4:00 PM EDT
Coffee Break
11th Floor Collaborative Space
4:00 - 4:45 PM EDT
Dynamical reduction for solitonic filaments
11th Floor Lecture Hall
Speaker
Ricardo Carretero, San Diego State University
Session Chair
Justin Holmer, Brown University
Abstract
In this talk we describe techniques for the dynamical reduction of soliton stripes in nonlinear spatio-temporal systems. The central idea is to cast reductions to accurately describe these structures with lower-dimensional models that are more easily tackled, both mathematically and computationally. In turn, the reduced models allow for an unprecedented description of the statics, stability, dynamics, and interactions of these structures.
Friday, May 01, 2026
9:00 - 9:45 AM EDT
TBA
11th Floor Lecture Hall
Speaker
Javier Gomez Serrano, Brown University
Session Chair
Vassilis Koukouloyannis, University of the Aegean
10:00 - 10:45 AM EDT
Identifying Phase Transitions in Dynamics and Data
Virtual
Virtual Speaker
Jason Bramburger, Concordia University
Session Chair
Vassilis Koukouloyannis, University of the Aegean
Abstract
Many complex dynamical systems undergo phase transitions that signal the emergence of coherent structures, ranging from synchronization in oscillator networks to coherent structures in fluid flows. In this talk, I present an optimization-based framework for identifying and characterizing such transitions using bounds on time-averaged observables obtained through polynomial optimization. The approach integrates auxiliary function methods and can be extended to incorporate data-driven techniques inspired by Koopman operator theory, enabling long-time behaviour to be inferred directly from governing equations or simulation data. Abrupt changes in these bounds over ranges of parameter values provide quantitative signatures of phase transitions and the onset of coherence. I demonstrate the method on representative and important examples, including the emergence of synchronization in coupled Kuramoto oscillators, data from a 9-mode model of shear flow, and full three-dimensional Navier–Stokes shear flow simulations, illustrating how the framework scales from low-dimensional models to high-dimensional PDE data and provides a unified lens for studying coherence across dynamical systems and data.
11:00 - 11:15 AM EDT
Coffee Break
11th Floor Collaborative Space
11:15 AM - 12:00 PM EDT
Data-Driven Structure Discovery in Nonlinear Wave Systems
11th Floor Lecture Hall
Speaker
Wei Zhu, Georgia Tech
Session Chair
Vassilis Koukouloyannis, University of the Aegean
Abstract
In this talk, we present a sequence of works on the use of machine learning to discover mathematical structure from data in nonlinear wave systems. These include the identification of governing equations, reduced-order closure models, conservation laws, Lax pairs, and integrability. We will present a range of machine learning approaches, highlighting both their capabilities and their limitations, along with strategies to address these challenges. The effectiveness of these methods will be demonstrated on several nonlinear wave systems, illustrating their potential for advancing data-driven scientific discovery and revealing hidden mathematical structure.
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- Personal car travel to ICERM from outside New England
- Multiple-destination plane ticket; does not include layovers to reach ICERM
- Arriving or departing from ICERM more than a day before or day after the program
- Multiple trips to ICERM
- Rental car to/from ICERM
- Flights on a Swiss, Japanese, or Australian airline
- Arriving or departing from airport other than PVD/BOS or home institution’s local airport
- 2 one-way plane tickets to create a roundtrip (often purchased from Expedia, Orbitz, etc.)
- Travel Maximum Contributions
- New England: $350
- Other contiguous US: $850
- Asia & Oceania: $2,000
- All other locations: $1,500
- Note these rates were updated in Spring 2023 and supersede any prior invitation rates.
- Reimbursement Requests
Request Reimbursement with Cube
Refer to the back of your ID badge for more information. Checklists are available at the front desk and in the Reimbursement section of Cube.
- Reimbursement Tips
- Scanned original receipts are required for all expenses
- Airfare receipt must show full itinerary and payment
- ICERM does not offer per diem or meal reimbursement
- Allowable mileage is reimbursed at prevailing IRS Business Rate and trip documented via Google Maps PDF
- Keep all documentation until you receive your reimbursement!
- Reimbursement Timing
6–8 weeks after all documentation is sent to ICERM. All reimbursements are reviewed by multiple Brown University offices.
- Reimbursement Deadline
Submissions must be received within 30 days of ICERM departure to avoid applicable taxes. No submissions are accepted after six months.