If you take a simple finite-dimensional Lie algebra g and tensor it with the Laurent polynomials in one variable, then you will get an infinite-dimensional Lie algebra known as a loop algebra.…
Modular tensor categories arise naturally in many areas of mathematics, such as conformal field theory, quantum groups and Hopf algebras, low dimensional topology, representations of braid groups, and they have…
Linear extensions of posets are important objects in enumerative and algebraic combinatorics that are difficult to count in general. Families of posets like straight shapes and $d$-complete posets have hook-length…
For this week, we have a special Algebra and Combinatorics meet & greet where we'll get to chat informally and discuss some ideas for the seminar and the upcoming talks. Join Zoom Meeting…
In this talk, I will share with you what kind of problems I work on and what's my motivation. We will talk about the representation theory of finite groups and…
Fusion categories are algebraic structures that generalize the representation categories of finite groups. I will explain how fusion categories have become involved in diverse areas of mathematics and physics, from…
I will discuss some algebraic aspects of recent work with Raphael Rouquier on a tensor product operation for categorified representations of U_q(gl(1|1)^+) and its connections to Heegaard Floer homology. Speaker’s…
First, I will make a general introduction to vertex algebras. Then, I will mention some results of recent work with Bojko Bakalov on Logarithmic vertex algebras. Jointly in person in…
I will tell you about my dissertation work on two variants of stable Grothendieck polynomials and their combinatorics. Relevant combinatorial objects include crystals (edge-labelled directed digraphs from representation theory), tableaux…
In a non-local game, two non-communicating players cooperate to convince a referee about a strategy that does not violate the rules of the game. A quantum strategy for such a…
The totally positive flag variety is the subset of the complete flag variety Fl(n) where all Plücker coordinates are positive. By viewing a complete flag as a sequence of subspaces…
We establish the conjecture of Reiner and Yong for an explicit combinatorial formula for the expansion of a Grothendieck polynomial into the basis of Lascoux polynomials. This expansion is a…
It is a classical result that the simple algebras in the category of finite dimensional vector spaces are precisely the n x n matrix algebras. The notion of algebras in more…
The theory of P-partitions was developed by Stanley to understand/solve several enumerations problems and representations theory problems. Together with the work of Gessel, this led to the development of the…
Jointly in person and virtually on Zoom. SAS 4201 for in-person participation. The Zoom link is sent out to the Algebra and Combinatorics mailing list, please contact Corey Jones at cmjones6@ncsu.edu to…
Coxeter groups were famously proven to be automatic by Brink and Howlett in 1993 and the automaticity of these groups has been an area of continued interest since. In this…
Lascoux polynomials are K-theoretic analogues of the key polynomials. They both have combinatorial formulas involving tableaux: reverse set-valued tableaux (RSVT) rule for Lascoux polynomials and reverse semistandard Young tableaux (RSSYT)…
Jointly in person and virtually on Zoom. SAS 2225 for in-person participation. The Zoom link is sent out to the Algebra and Combinatorics mailing list, please contact Corey Jones at cmjones6@ncsu.edu to…
BSTRctProbability distributions on the set of trees are fundamental in evolutionary biology, as models for speciation processes. These probability models for random trees have interesting mathematical features and lead to…
The story of noncrossing partitions starts with a Coxeter group W anda Coxeter element c. (If you're not familiar with Coxeter things, think: W is the symmetric group S_n and…