Algebra and Combinatorics Seminar: Jacob Matherne, NC State
SAS 4201Speaker’s webpage: https://math.sciences.ncsu.edu/people/jpmather/
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…
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…
Permutations $w$ in $S_n$ for which the (type-A) Schubert variety $\Omega_w$ is smooth are characterized by avoidance of the patterns 3412 and 4231. The smaller family of codominant permutations, those…
Petersen and Tenner defined the depth statistic for Coxeter group elements which, in the symmetric group, can be described in terms of a cost-minimization problem over the factorizations of a…
In 1995, Stanley introduced the chromatic symmetric function of a graph, a symmetric function analog of the classical chromatic polynomial of a graph. The Stanley-Stembridge e-positivity conjecture is a long-standing…
We will define quivers of type A-tilde, their representations, and exceptional collections of these representations. We will then introduce a combinatorial model of these representations, based on the one constructed…
Lam, Lee, and Shimozono (LLS) recently introduced backstable double Schubert polynomials to represent classes in the cohomology ring of the infinite flag variety. Using these polynomials, they introduce double Stanley…
A group is highly transitive if it admits a faithful, highly transitive action, that is an action which is k-transitive for all k>0. We will discuss some algebraic properties of…
We provide a generalization of Jouanolou duality that is applicable to a plethora of situations. The environment where this generalized duality takes place is a new class of rings, that…
Fun activity: Prepare a 5-10 minutes presentation on a math object that you want others to know about. That could include their definition, a couple of examples, some fun fact…
In Stanley’s seminal work “Cohen-Macaulay Complexes”, Stanley conjectured that all h vectors of matroid complexes are pure O-sequences. We constructed coparking functions on matroids with extra restrictions and showed that…
Quantum hardware has advanced to the point where it is now possible to perform simulations of small physical systems. Although the current capabilities are limited, given the rapid advancement it…
Consider the affine Lie algebra $\mathfrak{g}$ associated with the simple Lie algebra $sl(n)$ consisting of $n\times n$ trace zero matrices over the field of complex numbers. For every dominant integral…
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…