University of Washington

Motivated by a conjecture of Maglione–Voll from group theory, we introduce and study the Poincaré-extended ab-index. This polynomial generalizes both the ab-index and the Poincaré polynomial. For posets admitting R-labelings (a relaxation of EL...

In 1959, Farahat and Higman showed a remarkable property about the symmetric group: the structure constants for the center of the group algebra Sn depend polynomially on n and that there exists an infinite-dimensional algebra, which we call the...

The central objects in this talk are the descent polynomials of colored permutations on multisets, referred to as colored multiset Eulerian polynomials. These polynomials generalize the colored Eulerian polynomials that appear frequently in algebraic...

In this talk I will describe the first general construction of regular unimodular triangulations for matroid base polytopes. This construction extends to all integral generalized permutahedra. I will also discuss how this relates to White's...

Primitive integral Apollonian circle packings are fractal arrangements of tangent circles with integer curvatures. The curvatures form an orbit of a 'thin group,' a subgroup of an arithmetic group having infinite index in its Zariski closure. The...

Modern machine learning (ML) applications grapple with the challenges posed by high-dimensional datasets and high-dimensional parameter spaces. Stochastic gradient descent (SGD) and its variants have emerged as the go-to algorithms for optimizing in...

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...