Given a positive-definite even lattice Q, one can construct a lattice vertex algebra V. An important problem in vertex algebra theory and conformal field theory is to classify the representations of the subalgebra…
An important construction for (the information theoretic version of) semantic security is a "Biregular Irreducible Function" (BRI). These can be constructed from a complete biregular graph on $2^k d \times…
In this talk we want to consider a different kind of singularities in logarithmic vertex algebras. In vertex algebras many properties arise from the locality of their fields. In particular, this implies the…
We discuss the facial weak order, a poset structure that extends the poset of regions on a central hyperplane arrangement to the set of all faces of the arrangement which was first…
Modular tensor categories are rich mathematical structures. They are important in the study of 2D conformal field theory, arising as categories of modules for rational vertex operator algebras. The orbifold construction A-> A^{G} …
Let Q be an orientation of a type A Dynkin diagram. An eta map corresponding to Q is a surjection from the weak order on permutations to a Cambrian lattice…
We present a general formula describing the joint distribution of two permutation statistics—the peak number and the descent number—over any set of permutations whose quasisymmetric generating function is a symmetric…
The fundamental basis of the Hopf algebra of quasisymmetric functions, QSym, can be thought of in terms of shuffling permutations. We can think of QSym as having a basis indexed…
Independence polynomials are generating functions for the number of independent sets of each cardinality in a graph G. In addition to encoding useful information about the graph (such as the…
Chapoton triangles are polynomials in two variables defined by Coxeter-Catalan objects. These polynomials are related by some remarkable identities that only depend on the rank of the associated (finite) Coxeter system. The multidimensional…
In this talk, we will explain a (mysterious?) connection between the combinatorics of affine buildings and representation theory in type A. If a group acts simply and transitively on the…
We consider a finite group scheme G, and its associated representation category rep G. Here one can think of a finite discrete group, or an infinitesimal group scheme, such as…
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…