Mathematical Physics In-Person Seminar

Kasper Larsen – Rutgers University

Date/Time/Location

Thursday, October 1, 2026, 12:10 pm; Hill Center 705

Strict SDE Comparison for Cusp Coefficients and Counterexamples

We provide a tractable sufficient condition for strict comparison for solutions of the one-dimensional stochastic differential equation dX = sigma(X)dB, with initial condition x in an interval I, for sigma positive and continuous. Our proof is based on a two-dimensional Lyapunov argument, which allows us to prove strict comparison for some coefficients in the local Sobolev space W1p, for p between 1 and 2. We illustrate using sigma of x equal to 1 plus the absolute value of x to the power beta, for beta between 0 and 1, and show that strict comparison holds if and only if beta is at least one half. We give examples showing that neither local W1p regularity for p between 1 and 2 nor Hölder regularity of order beta between one half and 1 is sufficient for strict comparison, even when combined with boundedness, uniform ellipticity, global strong existence, and pathwise uniqueness.

Anirvan Sengupta – Rutgers University

Date/Time/Location

Thursday, September 24, 2026, 12:10 pm; Hill Center 705

In-context Denoising, Attention and Diffusion

Modern neural networks can have enough parameters to memorize their training data, yet often generalize remarkably well. I will discuss this tension from a statistical-physics perspective, focusing on attention mechanisms and their relation to associative memory. I will first consider an in-context denoising problem for a one-layer transformer. For several simple data models, the Bayes-optimal denoiser can be derived explicitly and represented by linear or softmax attention, providing a direct connection to modern Hopfield models. In this picture, generalization is associated with a crossover of the Hopfield energy landscape from isolated stored patterns to a representation of the underlying data distribution. I will then discuss multilayer attention-only dynamics, where all samples evolve together. In an appropriate continuum limit, the resulting self-attractive dynamics can be related to anti-diffusion, connecting attention to score-based denoising and empirical Bayes. This suggests a unified view of associative memory, attention, and diffusion-based generative modeling.

Luc Rey-Bellet – UMASS Date/Time/Location Thursday, April 30, 2026, 12:10 pm; Hill Center 705 Proximal optimal transport divergences for generative modeling and sampling. The motivation for this work comes from generative modeling and sampling problems where the target distributions are

Alex Kontorovich - Rutgers Date/Time/Location Thursday, April 23, 2026, 12:10 pm; Hill Center 705 Arithmetic Hyperbolic 3-Manifolds A construction due to Thurston assigns a hyperbolic 3-manifold to any Euclidean polyhedron. A basic question is to determine which such are arithmetic.

Lawrence Frolov – Rutgers Date/Time/Location Thursday, April 16, 2026, 12:10 pm; Hill Center 705 Overcoming the arrival time quantum Zeno effect In classical mechanics, there is a conceptually clear method for computing the time at which a particle will arrive

David Huse – Princeton University Date/Time/Location Thursday, April 9, 2026, 12:10 pm; Hill Center 705 Thermal first-order phase transitions and the eigenstate thermalization hypothesis A many-body system with a thermal first-order phase transition exhibits an extensive discontinuity in the energy

Konstantin Mischaikow - Rutgers Date/Time/Location Thursday, April 2, 2026, 12:10 pm; Hill Center 705 Rigorously Characterizing Dynamics with Machine Learning The identification of dynamics from time series data is a problem of general interest. It is well established that dynamics

Sanchit Chaturvedi - NYU Date/Time/Location Thursday, March 26, 2026, 12:10 pm; Hill Center 705 Linear stability of traveling Maxwellians for Landau equation with very soft potentials In this talk, I will discuss the problem of linear stability of traveling Maxwellians

Valerio Lucarini - University of Leicester Date/Time/Location Thursday, March 12, 2026, 12:10 pm; Hill Center 705 Linear Response and Optimal Fingerprinting for Nonautonomous Systems We provide a link between response theory, pullback measures, and optimal fingerprinting method that paves the

Federico Bonetto – Georgia Institute of Technology Date/Time/Location Thursday, March 5, 2026, 12:10 pm; Hill Center 705 Approach to equilibrium for a particle interacting with a harmonic thermal bath We study the long time evolution of the position-position correlation function

Matt Young - Rutgers Date/Time/Location Thursday, February 26, 2026, 12:10 pm; Hill Center 705 Eisenstein series and equidistribution Quantum chaos predicts that high energy eigenfunctions of the Laplacian on a negatively curved surface should exhibit chaotic behavior. For the modular

Natan Andrei – Rutgers University Date/Time/Location Thursday, February 19, 2026, 12:10 pm; Hill Center 705 Thermodynamics in a split Hilbert space: Quantum impurity in interacting environments A rich phase diagram arises when a quantum spin impurity is placed in an

Facundo Mémoli – Rutgers University Date/Time/Location Thursday, February 12, 2026, 12:10 pm; Hill Center 705 Distance distributions and inverse problems for metric measure spaces Many problems in data science—shape analysis, object recognition, and object classification—require comparing probability distributions that live

David Vanderbilt - Rutgers University Date/Time/Location Thursday, February 5, 2026, 12:10 pm; Hill Center 705 Theory of adiabatic phonon-magnon coupling in magnetic materials Conventional approaches for computing lattice dynamics do not fully account for the effects of time-reversal symmetry breaking

Jeffry Kahn – Rutgers University Date/Time/Location Thursday, January 29th, 2026, 12:10 pm; Hill Center 705 Thresholds for graph containment Thresholds have been central to the study of random graphs and related structures since its initiation by Erdos and Renyi in

Christian Maes – KU Leuven Date/Time/Location Thursday, December 11th, 2025, 12:10 pm; Hill Center 705 Response-fluctuation relations for driven systems We discuss quasistatic response for nonequilibrium systems satisfying local detailed balance. We give the example of thermal response and an

Roger Nussbaum – Professor Emeritus, Rutgers University Date/Time/Location Thursday, December 4th, 2025, 12:10 pm; Hill Center 705 The Hausdorff Dimension Spectrum of Continued Fractions and Their Generalizations If T is a nonempty set of of positive integers, denote by dim(T)

Gerald Goldin – Rutgers University Date/Time/Location Thursday, November 20th, 2025, 12:10 pm; Hill Center 705 A Universal Kinematical Group for Quantum Mechanics and Some Consequent Anyonic Structures This talk first describes recent results with David Sharp (Los Alamos), where we

Avraham Soffer – Rutgers University Date/Time/Location Thursday, November 13th, 2025, 12:10 pm; Hill Center 705 Global Self-Similar solutions, Breakdown of Asymptotic Completeness-New Physics? For Schrödinger-type equations with time-dependent, spatially local interactions — including nonlinear cases — there exist solutions that