Seminars Sorted by Series

This seminar will cover such topics as: Jones-Witten knot invariants, large N duality, knot invariants and Gromov-Witten invariants, topological vertex, Nekrasov's partition function and geometric engineering. The first lecture will give an overview...

This seminar is intended to cover background material or serve as a discussion session for the seminar "Yang-Mills theory for mathematicians", which will start on the following week. The first talk will give a brief overview of the concepts of...

I will give an overview of what is going to be discussed in the seminar during the semester, and start an introduction to the theory. No previous familiarity with geometric Langlands will be assumed.

The goal of the seminar is to cover the formalism of chiral algebras and related constructions that will be used in later talks in geometric Langlands seminar. In this talk an overview of representation theory of affine Lie algebras will be given...

An overview will be continued by a discussion of basic notions of quantum field theory (path integral, Feynman diagrams etc.)

This will be a discussion session for Gukov's talk, and/or a lecture on the background material, such as Gaussian integrals of the free theory, formal Feynman expansions etc.

Jones-Witten knot invariants and, time permitting, Chern-Simons perturbation theory will be discussed.

Fluctuations of the current of one dimensional non equilibrium diffusive systems are well understood. After a short review of the one dimensional results, the talk will try to show that the statistics of these fluctuations are exactly the same in...

Previous studies of kinetic transport in the Lorentz gas have been limited to cases where the scatterers are distributed at random (e.g. at the points of a spatial Poisson process) or at the vertices of a Euclidean lattice. In this talk I will...

This will be a background talk on the Kardar-Parisi-Zhang equation and its universality class.

I will start with discussing the relation between a class of disorder-generated multifractals and logarithmically-correlated random fields and processes. An important example of the latter is provided by the so-called "\(1/f\) noise" which, in...

This will be a background talk on the Kardar-Parisi-Zhang equation and its universality class.

Our goal is to explain how certain basic representation theoretic ideas and constructions encapsulated in the form of Macdonald processes lead to nontrivial asymptotic results in various `integrable'; probabilistic problems. Examples include dimer...

Our goal is to explain how certain basic representation theoretic ideas and constructions encapsulated in the form of Macdonald processes lead to nontrivial asymptotic results in various `integrable'; probabilistic problems. Examples include dimer...

An isolated quantum many-body system may be a reservoir that thermalizes its constituents. I will explore an example of the interplay of this thermalization and spontaneous symmetry-breaking, in the ferromagnetic phase of an infinite-range quantum...

In the early 1960's Dyson and Mehta found that the CSE relates to the COE. I'll discuss generalizations as well as other settings in random matrix theory in which \(\beta\) relates to \(4/\beta\).

We develop spectral theory for the generator of the \(q\)-Boson particle system. Our central result is a Plancherel type isomorphism theorem for this system; it implies completeness of the Bethe ansatz in infinite volume and enables us to solve...

The quantum random energy model is a random matrix of Schroedinger type: a Laplacian on the hypercube plus a random potential. It features in various contexts from mathematical biology to quantum information theory as well as an effective...

I discuss a renormalization group method to derive diffusion from time reversible quantum or classical microscopic dynamics. I start with the problem of return to equilibrium and derivation of Brownian motion for a quantum particle interacting with...

What is the volume of the set of singular symmetric matrices of norm one? What is the probability that a random plane misses this set? What is the expected "topology" of the intersection of random quadric hypersurfaces? In this talk I will combine...

The study of the Gaussian limit of linear statistics of eigenvalues of random matrices and related processes, like determinantal processes, has been an important theme in random matrix theory. I will review some results starting with the strong...

In cryo-electron microscopy (cryo-EM), a microscope generates a top view of a sample of randomly-oriented copies of a molecule. The cryo-EM problem is to use the resulting set of noisy 2D projection images taken at unknown directions to reconstruct...

Based on joint work with A. Guionnet (MIT). The beta ensemble is a particular model consisting of N strongly correlated real random variables. For specific values of beta, it is be realized by the eigenvalues of a random hermitian matrix whose...

We consider a system of harmonic oscillators with stochastic perturbations of the dynamics that conserve energy and momentum. In the one dimensional unpinned case, under proper space-time rescaling, Wigner distribution of energy converges to the...

I will discuss the proof by Yang Kang and myself of diffusion for the Markov Anderson model, in which the potential is allowed to fluctuate in time as a Markov process. However, I want to highlight the method of the proof more than the result itself...

Inspired by recent work of Alberts, Khanin and Quastel, we formulate general conditions ensuring that a sequence of multi-linear polynomials of independent random variables (called polynomial chaos expansions) converges to a limiting random variable...

We construct a \(\mathrm{KPZ}_t\) line ensemble -- a natural number indexed collection of random continuous curves which satisfies a resampling invariance called the H-Brownian Gibbs property (with \(H(x)=e^x\)) and whose lowest indexed curve is...

We discuss two random decreasing sequences of continuous functions in two variables, and how they arise as the scaling limit from corners of a (real / complex) Wigner matrix undergoing stochastic evolution. The restriction of the second one to...

This will be an informal session in which we will try to answer questions from the audience on topics around KPZ.

After a short introduction to some ideas on quantum probability theory I discuss the roles played by loss of information and entanglement in the emergence of facts in quantum-mechanical experiments and observations. Besides explaining why...

I will describe the general ideas behind exponential asymptotic methods, their recent developments, and a number of open problems that were solved in the last few years using them, such as the behavior of Hydrogen atoms in time periodic fields and...

In several naturally occurring (infinite) point processes, we show that the number (and other statistical properties) of the points inside a finite domain are determined, almost surely, by the point configuration outside the domain. This curious...

The stochastic Burgers equation (equivalent to the one-dimensional KPZ equation) is a hyperbolic conservation law with random currents. In applications, one often has to deal with several conservation laws, a little explored case. We discuss several...

We prove a quantitative Brunn-Minkowski inequality for sets \(E\) and \(K\), one of which, \(K\), is assumed convex, but without assumption on the other set. We are primarily interested in the case in which \(K\) is a ball. We use this to prove an...

We will describe formulas for the asymmetric simple exclusion process (ASEP) starting from half-flat and flat initial data. The formulas are for the exponential moments of the height function associated with ASEP. They lead to explicit formulas for...

The (weakly) self-avoiding walk is a basic model of paths on the d-dimensional integer lattice that do not intersect (have few intersections), of interest from several different perspectives. I will discuss a proof that, in dimension 4, the...

In the 90's numerical simulations have unveiled interesting properties of random ensembles of constraint satisfaction problems (satisfiability and graph coloring in particular). When a parameter of the ensemble (the density of constraints per...

I will present results on the study of various temporal correlation functions of a tagged particle in a one-dimensional system of interacting particles evolving with Hamiltonian dynamics and with initial conditions chosen from thermal equilibrium.

We review some of the connections, established and expected between random matrix theory and Zeta functions. We also discuss briefly some recent Universality Conjectures connected with families of L-functions.

I will present recent results on a non-relativistic Hamiltonian model of quantum friction, about the motion of an invading heavy tracer particle in a Bose gas exhibiting Bose Einstein condensate. We prove the following observations: if the initial...

I will describe several properties (structural and/or computational) which are satisfied by random matrices almost surely, but for which we have no concrete examples of such matrices. My hope is that the audience will be intrigued and interested in...

We prove that the logarithm of Fourier series with random signs is integrable to any positive power. We use this result to prove the angular equidistribution of the zeros of entire functions with random signs (and more generally the almost sure...

We consider an harmonic chain perturbed by an energy conserving noise and show that after a space-time rescaling the energy-energy correlation function is given by the solution of a skew-fractional heat equation with exponent 3/4.

According to first principle quantum mechanics, the evolution of N fermions (particles with antisymmetric wave function) is governed by the many body Schroedinger equation. We are interested, in particular, in the evolution in the mean field regime...

We compute new families of time-periodic and quasi-periodic solutions of the free-surface Euler equations involving extreme standing waves and collisions of traveling waves of various types. A Floquet analysis shows that many of the new solutions...