University of Washington

Tadao Oda conjectured that every smooth polytope, in any dimension, has the Integer Decomposition Property. Beck et al. previously showed that smooth polytopes which are both 3-dimensional and centrally symmetric have this property. We show this...

In characteristic zero, the Hopf algebra of quasisymmetric functions QSym is isomorphic to the shuffle algebra of compositions Sh, and isomorphisms between them can be specified via shuffle bases of QSym. We give characterizations of shuffle bases...

The Schensted correspondence is a bijection between permutations in Sn and pairs of standard Young tableaux (P,Q) with n boxes which have the same shape. This bijection has remarkable properties in algebraic and enumerative combinatorics. Motivated...

A harmonic function of one variable is a linear function. A harmonic function of two variables is the real or imaginary part of an analytic function. A harmonic function of n variables is a function u satisfying \frac{\partial^{2}u}{\partial x_{1}^{2...

Building trees to represent or to fit distances is a critical component of phylogenetic analysis, metric embeddings, approximation algorithms, geometric graph neural nets, and the analysis of hierarchical data. We summarize several recent efforts to...

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...

Alternating sign matrices (ASMs) were introduced by Robbins and Rumsey in the early 1980s. Together with Mills they conjectured an enumerative formula for the number of ASMs of size n×n, which was proved independently by Zeilberger and Kuperberg...

We show that various classical theorems of real/complex linear incidence geometry, such as the theorems of Pappus, Desargues, Möbius, and so on, can be interpreted as special cases of a single "master theorem" that involves an arbitrary tiling of a...

Nonsmoothness and nonconvexity are significant challenges in large-scale optimization problems, such as training neural networks and solving inverse problems in computational imaging. Although first-order methods are commonly used to address these...

This short workshop is being hosted at the University of Washington and is in honor of Prof Adrian Lewis in recognition of his fundamental contributions to nonsmooth optimization Schedule: Aug 9: 9 am -- 5pm & Invited talks at the University of...