University of Washington

Algebraic geometry is the study of geometric objects defined as the solution set of a system of polynomial equations p1,…,pr∈F[x1,…,xn] where F is an algebraically closed field. After recent spectacular progress in the classification of varieties...

In number theory and diophantine geometry, the theory of "heights" is essential in studying finiteness questions. Roughly, they capture the "arithmetic complexity" of the object of study. We give a formula relating various notions of heights of...

Many results in extremal graph theory can be formulated as inequalities on graph densities. While many inequalities are known,many more are conjectured. A standard tool to establish an inequality is to write the expression whose nonnegativity needs...

I will discuss recent new developments in De Giorgi Conjecture for Allen-Cahn equation. In dimensions up to 10, we shall establish the C2,α estimates of level sets for stable solutions of Allen-Cahn. By applying reverse gluing method we show that the...

Northwest Probability Seminars are mini-conferences held at the University of Washington and organized in collaboration with the Oregon State University, the University of British Columbia and the University of Oregon. There is no registration fee...

The optimal transport problem provides a fundamental and quantitative way to measure the distance between probability distributions. Recently, it has been successfully used to analyze the evolutionary dynamics in physics and biology. Motivated by...

The theory of large deviations provides with a way to compute asymptotically the probability that an interacting particle system moves from a given configuration to another one over a fixed time interval. The problem of finding the most likely...

Entropic optimal transport has received a lot of attention in recent years and has become a popular framework for computational optimal transport thanks to the Sinkhorn scaling algorithm. In this talk, I will discuss the multi-marginal case which...

Generative models such as Generative Adversarial Nets (GANs), Variational Autoencoders and Normalizing Flows have been very successful in the unsupervised learning task of generating samples from a high-dimensional probability distribution. However...

Stein’s method is a set of techniques for bounding distances between probability measures via integration-by-parts formulas. It was introduced by Stein in the 1980s for bouding the rate of convergence in central limit theorems, and has found many...