Algebra and Combinatorics Seminar: Spencer Daugherty, NC State, Thesis Defense
SAS 4201Speaker’s webpage: https://spdaugherty.github.io/
Speaker’s webpage: https://spdaugherty.github.io/
In this talk we define a new category of matroids, by working on matroid polytopes and rank preserving weak maps. This lets us introduce the concept of categorical valuativity for…
Speaker's website
Polyhedral fans are geometric objects, which arise naturally in many areas of mathematics, for example in toric geometry, the theory of hyperplane arrangements and representation theory. In many cases, there…
The pop-stack sorting method takes an ordered list or permutation and reverses each descending run without changing their relative positions. In this talk we will review recent combinatorial results on…
A "frieze" is an infinite strip of numbers satisfying certain determinantal identities, or any one of several generalizations of this idea. In this talk, I will give an introduction to…
Cauchy's determinantal identity (1840s) expands via Schur polynomials the determinant of the matrix f, where f(t) = 1/(1-t) is applied entrywise to the rank-one matrix u v^T = (u_i v_j). This theme has…
We will give an introduction to nets of associative algebras over discrete metric spaces, which arise in mathematical physics as axiomatizations of the observables content of quantum field theories over…
The theory of integral closure of ideals, originating in the early twentieth century with work of Krull, Zariski, Rees, and others, remains a vibrant area of research in algebraic geometry,…
A representation of the category of finite sets is a linear algebraic object, which roughly consists of a sequence of representations V_n of the symmetric group S_n related by transition…
Motivated by the problem of classifying quantum symmetries of non-semisimple, finite-dimensional associative algebras, we define a notion of connection between bounded quivers and build a bicategory of bounded quivers and…
Finding combinatorial interpretations for the structure constants of Schubert polynomials is a long-standing open problem in algebraic combinatorics. In the case where one of the Schubert polynomials is a Schur…
Noncrossing partitions and nonnesting partitions are both counted by Catalan numbers. Noncrossing partitions on admit a natural cyclic action of order 2n, induced by the Kreweras complement. Nonnesting partitions admit a natural toggle-based…
The Schur functions are an important basis of the ring of symmetric functions, and Schur’s Q-functions enjoy many analogous properties as a basis of the subring Gamma. We will begin…
The Hilbert scheme of d points on a smooth variety X, denoted by Hilb^d(X), is an important moduli space with connections to various fields, including combinatorics, enumerative geometry, and complexity…
Speaker's website: https://dleon.combinatoria.co/
Speaker's website: https://www.ewbates.com/
Speaker's website: https://sites.google.com/view/ferroniluis
Speaker's website: https://jack-jeffries.github.io/
Speaker's website: https://pi.math.cornell.edu/~karola/