Symplectic geometry, physics and algebraic combinatorics

Rutgers University New Brunswick, New Brunswick NJ

Investigators

Abstract

Abstract Award: DMS-0093647 Principal Investigator: Christopher T. Woodward The principal investigator plans to develop the theory of group actions on symplectic manifolds and geometric invariant theory, and extend applications to certain 2d conformal field theories and algebraic combinatorics. In particular, he will investigate the theory of loop group actions, group-valued moment maps, and relations to the Wess-Zumino-Witten model in conformal field theory and cohomology pairings on moduli spaces of flat connections; the asymptotic limit of the quantum 6j symbols; and decomposition of products of conjugacy classes in disconnected compact groups and twisted forms of quantum cohomology. He will integrate his research with a variety of educational projects, such as dynamical systems in the calculus and linear algebra sequence at Rutgers; strengthening the joint major with computer science; laboratory activities in the undergraduate curriculum and evaluation of their effectiveness. Symplectic geometry is the mathematical framework for the study of classical mechanics, and in particular Hamiltonian dynamical systems. Woodward will undertake a number of projects to develop the field and its role in the undergraduate and graduate curriculum. He will seek to understand symmetries, especially of infinite dimension, in this setting. Possible applications outside of mathematics are the development of new computational techniques in conformal field theory, an important topic in recent high-energy theoretical physics, and improvement of the efficiency of wireless communication, via the construction of better packings in the unitary group.