Reading’s shard intersection order is a lattice structure on a finite Coxeter group which is weaker than the weak order. This structure also appears in the representation theory of finite-dimensional algebras as the inclusion order on certain subcategories of modules. Algebraically, the cover relations of this lattice are traversed by applying a “reduction operation” associated…

We describe an algorithm to compute Whitney stratifications of real algebraic varieties. The basic idea is to first stratify the complexified version of the given real variety using conormal techniques, and then to show that the resulting stratifications admit a description using only real polynomials. This method also extends to stratification problems involving certain basic…

Speaker’s webpage: https://math.sciences.ncsu.edu/people/jpmather/

This talk will introduce cluster algebras, with an emphasis on their combinatorics, and describe a recent joint result with Vincent Pilaud and Sibylle Schroll. At the heart of a cluster algebra is a complicated, branching recursion that defines cluster variables (certain rational functions organized into finite sets called clusters). The recursion looks bizarre at first…

Quantum cellular automata (QCA) are models of discrete-time unitary dynamics of quantum spin systems. They can be characterized algebraically as certain automorphisms of the associative algebra generated by local observables of a spin system. We will give a gentle introduction to this topic, and explain some of our recent contributions to the problem of classification…