University of Washington

Random high-dimensional cost functions and random probability distributions arise in a number of applied fields. For instance, in high-dimensional statistics, an M-estimator is the solution of a random optimization problem (the randomness being...

A useful way of producing samples from a given measure ν on a state space Ω is by providing a Markov chain whose stationary measure in ν. In order to be able to sample efficiently, one needs to show that the chain "mixes" quickly in terms of the rate...

Topology is the branch of mathematics concerned with shapes and their spatial properties. In this talk I’ll show how several ideas from classic algebraic topology – like cohomology, classifying spaces and vector bundles – can be used in machine...

Graphs are ubiquitous in modern applications---including some very large graphs. This leads one to wonder, "How can we understand such large graphs?" One prevalent idea is to observe them locally: to count how many times certain substructures appear...

Solving a longstanding problem on equiangular lines, we determine, for each given fixed angle and in all sufficiently large dimensions, the maximum number of lines pairwise separated by the given angle. A key ingredient is a new result in spectral...

The common theme of this summer school is the mathematics of Monge-Kantorovich optimal transport (OT). The stunning mathematical development of OT has recently permeated into several fields of applications. Our speakers, chosen from the fields of...