Seminars Sorted by Series

Conformal blocks are fundamental objects in the conformal bootstrap program of 2D conformal field theory and are closely related to four dimensional supersymmetric gauge theory.

In this talk, I will demonstrate a probabilistic construction of a 1...

I will explain recent progress on computing approximate ground states of mean-field spin glass Hamiltonians, which are certain random functions in high dimension. While the asymptotic ground state energy OPT is given by the famous Parisi formula...

First-passage percolation studies the geometry obtained from a random perturbation of Euclidean geometry. In the discrete planar setting, one assigns random, independent and identically distributed, lengths to the edges of the lattice Z^2 and...

The interchange process \sigma_T is a random permutation valued process on a graph evolving in time by transpositions on its edges at rate 1. On Z^d, when T is small all the cycles of the permutation \sigma_T are finite almost surely. In dimension d...

We consider a general system of interacting random loops which includes several models of interest, such as the spin O(N) model, the double dimer model, random lattice permutations, and is related to the loop O(N) model and to the interacting Bose...

The XY and the Villain models are models which exhibit the celebrated Kosterlitz-Thouless phase transitions in two dimensions. The spin wave conjecture, originally proposed by Dyson and by Mermin and Wagner, predicts that at low temperature, spin...

This is joint work with Haolin Shi (Yale). 3-webs are bipartite, trivalent, planar graphs. They were defined and studied by Kuperberg who showed that they correspond to invariant functions in tensor products of $SL_3$-representations. Webs and...

A meandric system of size $n$ is the set of loops formed from two arc diagrams (non-crossing perfect matchings) on $\{1,\dots,2n\}$, one drawn above the real line and the other below the real line. Equivalently, a meandric system is a coupled...

Lévy matrices are symmetric random matrices whose entries are in the domain of attraction of an \alpha stable law. For \alpha 1, it had been predicted that these matrices exhibit an Anderson transition, also called a mobility edge, a point in the...

It all began with card shuffling. Diaconis and Shahshahani studied the random transpositions shuffle; pick two cards uniformly at random and swap them. They introduced a Fourier analysis technique to prove that it takes $1/2 n \log n$ steps to...

We discuss new results on lozenge tilings on an infinite cylinder, which may be analyzed using the periodic Schur process introduced by Borodin. Under one variant of the q^vol measure, corresponding to random cylindric partitions, the height...

Conformal blocks are objects of fundamental importance in the bootstrap approach for exact solvability of 2D conformal field theory (CFT).  In this talk, we will present novel probabilistic expressions for them using the Gaussian free field in lieu...

For each central charge $c\in (0,1]$, we construct a conformally invariant field which is a measurable function of the local time field $\mathcal{L}$ of the Brownian loop soup with intensity $c$ and i.i.d. signs given to each cluster. This field is...

We consider a Poisson point process on $R^d$ with intensity lambda for $d>=2$. On each point, we independently center a ball whose radius is distributed according to some power-law distribution mu. When the distribution mu has a finite d-moment...

We will discuss stochastic quantization i.e. Langevin dynamic of the Yang-Mills model on two and three dimensional torus. This is described by a Lie algebra valued stochastic PDE driven by space-time white noise. We construct $(local)$ solution to...

I will start by introducing and motivating the (two-component) Coulomb gas on the d-dimensional lattice $Z^d$. I will then present some puzzling properties of the fluctuations of this Coulomb gas. The connection of this model with integer-valued...

Lecture 1: 10:15-11:15

On The Cover Time of Random Walks on Graphs

How long does it take for a random walk to cover all the vertices of a graph? 

And what is the structure of the uncovered set (the set of points not yet visited by the walk) close...

I will discuss exact solvability results (in a sense) for scaling limits of interface crossings in critical random-cluster models in the plane with various general boundary conditions.

The results are rigorous for the FK-Ising model, Bernoulli...

Speaker #1 (Lawler): I will present a somewhat novel approach to known relationships (in works of Sheffield, Miller, and others) between SLE and GFF, the exponential of the GFF (quantum length/area), and Minkowski content of paths. The Neumann GFF...

This is a joint work with Reza Gheissari (Northwestern) and Aukosh Jagannath (Waterloo), Outstanding paper award at NeurIPS 2022. We study the scaling limits of stochastic gradient descent (SGD) with constant step-size in the high-dimensional regime...

Liouville conformal field theory is a CFT with central charge c>25 and continuous spectrum, its correlation functions on Riemann surfaces with marked points can be expressed using the bootstrap method in terms of conformal blocks. We will explain...

In Euclidean geometry, bisectors are perpendicular lines. In random plane geometry, the situation is more complicated. I will describe bisectors in the directed landscape, the universal geometry in the KPZ class. These help answer some open...

Through the random matrix analogy, Fyodorov, Hiary and Keating conjectured very precisely the typical values of the Riemann zeta function in short intervals of the critical line, in particular their maximum. Their prediction relied on techniques...