University of Washington

Reconstructing simplicial complexes from partial information has been a problem of interest for decades. A triangulation of a d-dimensional sphere is obtained by gluing a collection of d-dimensional simplices (“higher dimensional triangles”) along...

Density functional theory (DFT) is one of the workhorses of quantum chemistry and material science. In principle, the joint probability of finding a specific electron configuration in a material is governed by a Schrödinger wave equation. But...

The Gromov-Wasserstein (GW) distance quantifies dissimilarity between metric measure (mm) spaces and provides a natural alignment between them. As such, it serves as a figure of merit for applications involving alignment of heterogeneous datasets...

Tropicalization is a way to understand the asymptotic behavior of algebraic (or semi-algebraic) sets through polyhedral geometry. In this talk, I will talk about the tropicalization of the principal minors of positive semidefinite matrices. This...

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...