Multiline queues were introduced by Ferrari and Matrin as a tool for understanding the steady state of the Totally Asymmetric Simple Exclusion Process (TASEP) on a ring. Since then, they have attracted independent…
A Kirillov-Reshetikhin(KR) module is a certain finite dimensional U_q'(\mathfrak{g}) module that is determined by its Drinfeld polynomials. KR modules are an important class of modules for quantum groups with many applications to Mathematical…
Yangians are one of the main examples of quantum groups introduced by Drinfeld and have found applications in combinatorics, representation theory and algebraic geometry. It is well-known that the R-matrix presentation of…
The pancake graph has the elements of the symmetric group as vertices and there is an edge between two permutations if there is a prefix reversal that transforms one permutation into the other. One…
Kirillov-Reshetikhin (KR) modules are a special class of finite-dimensional modules for affine Lie algebras that have deep connections with mathematical physics. One important aspect is that they are conjectured to…
In their celebrated 1993 paper, Brink and Howlett proved that all finitely generated Coxeter groups are automatic. In particular, they constructed a finite state automaton recognising the language of reduced…
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…