University of Washington

We consider the problem of minimizing the average of a large number of smooth but possibly non-convex functions. For machine learning applications, the loss functions are mostly non-negative and thus can be written as the composition of the square...

Recent decades have seen a lot of progress in the "orbital circle method" attacking classical problems from dynamics, geometry, and number theory under the umbrella of "thin groups". There was always a danger that the circle method was too crude a...

The Birnbaum Lecture in Probability will be delivered by Robin Pemantle (University of Pennsylvania) in 2023. Northwest Probability Seminars are mini-conferences held at the University of Washington and organized in collaboration with the Oregon...

A basic question in algebraic geometry is whether there can be any non-constant maps between (smooth, projective) varieties of different types. I will explain some basic and some more sophisticated obstructions to the existence of such maps, mostly...

The moduli space \M_g of genus g curves (or Riemann surfaces) is a central object of study in algebraic geometry. Its cohomology is important in many fields. For example, the cohomology of M_g is the same as the cohomology of the mapping class group...

I will talk about: New efficient algorithms for quantum state tomography (the quantum analogue of estimating a probability distribution). Why you should care about the difference between total variation distance and Hellinger distance and KL...

A nodal real algebraic curve in the affine plane is called expressive if its defining polynomial has the smallest number of critical points that is allowed by the topology of the set of real points of the curve. This notion can be viewed as a "global...

Our world swirls with percentages, ratios, and graphs. These numbers are often presumed to be objective reflections of reality. But they are not. To measure a human-designed society requires human-designed measures, with all attendant foibles folded...

The periodic orbits and their structure are fundamental features of a dynamical system. In an algebraic setting, where the system is defined by polynomials, we can use tools from algebraic or arithmetic geometry to study these orbits. Important...

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...