Algebraic combinatorics basics
Abstract: Algebraic Combinatorics sits at the intersection of Combinatorics and Representation Theory and Algebra, using algebraic methods to answer combinatorial questions and employs tools from discrete mathematics to study problems in group theory and representation theory.
In this minicourse we will start with introducing basic tools and theorems from Algebraic Combinatorics which have seen wide applications in Statistical Mechanics: symmetric function theory, representation theory of the symmetric group, the RSK algorithm and nonintersecting lattice paths etc. We will then see how we can use them to derive probabilistic results like limit behavior in dimer models (mainly lozenge tilings). We will also discuss the application of probabilistic methods in enumerate asymptotically combinatorial objects.