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. Affine Lie algebras are the central extensions of such loop algebras and their representations have been of interest to several mathematicians. What happens if we tensor g with…

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 important applications in condensed matter physics, modeling topological phases of matter. In this talk, I will start by introducing the relevant concepts (modular, braided and…

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 product formulas to count linear extensions, whereas families like skew shapes have determinant or positive sum formulas like the Naruse hook length formula from 2014.…