The goal of this project is training of undergraduate students, graduate students, and postdocs at the research interface of combinatorics, geometry, and representation theory. This area includes enumerative geometry, geometric representation theory of infinite dimensional Lie algebras, corresponding quantized universal enveloping algebras, and of Hecke algebras. On the combinatorial side we will also focus on algebraic combinatorics and its applications. All these areas have seen fascinating progress in the last decade.
The project will be conducted with active involvement of graduate and undergraduate students and post-docs. These areas of mathematics are closely related to many recent developments in mathematical physics (the mathematical side of theoretical physics), mostly to quantum field theory, string theory, and statistical mechanics. Combinatorial problems which will be addressed also have direct applications in biology, for instance in the study of phylogenetic trees. This grant (in combination with other grants) will be used to fund a number of training workshops and master-classes on hot research topics aimed at post-doctoral fellows, graduate, and undergraduate students.
