The Mukhin-Varchenko and Rogers-Ramanujan conjectures (2011-2016)

This proposal aims to prove two deep conjectures in pure mathematics. These conjectures - The Mukhin-Varchenko conjecture, and the existence of Rogers-Ramanujan identities for affine Kac-Moody Lie algebras - have a very rich history and are connected to many different branches of mathematics, such as combinatorics, number theory and representation theory. Additionally both conjectures are strongly tied to the theory of orthogonal polynomials and it is through this theory that we aim to resolve them. Progress towards either of these conjectures would be a major major advance in pure mathematics, and is expected to have applications and important consequences for all of the different fields of mathematics involved.