The combinatorics of seaweed algebras Seaweed algebras form a class of Lie algebras for which a number of algebraic invariants can be computed combinatorially. One such invariant is the index, an important algebraic invariant which is notoriously difficult to compute. …
SIMPLE CLOSED GEODESICS ON HYPERBOLIC SURFACES Many of the 21st century spectacular advances in geometry and topology involve the study of simple closed geodesics on hyperbolic surfaces (Thurston, Mirzakhani, etc). I will tell you about one difficult little aspect of …
From Polyominoes to Fibonacci and Catalan Numbers Polyominoes are simple geometric objects that lead to many interesting and sometimes surprisingly difficult problems in discrete mathematics and theoretical computer science. In this talk, I will introduce polyominoes and discuss two classical …
Bridging the Gap Between Stable Marriage and Stable Roommates: A Parameterized Algorithm for Optimal Stable Matchings An instance of the Stable Roommates (SR) problem consists of 2n agents, each with a preference list that linearly orders the other agents. The …