Doug Pickrell: Research Interests

  • Geometry and Lie groups, especially infinite dimensional groups, such as loop groups and the Virasoso group, which are relevant to mathematical physics.
  • Ergodic theory, and invariant measures for group actions (such as the mapping class group).
  • Geometric approaches to two dimensional quantum field theory (e.g. Segal's axioms), and related ideas from string theory.
  • Conformal field theory, conformally invariant measures on self-avoiding loops on Riemann surfaces, conformal loop ensembles, Schramm-Loewner evolution.
  • Yang-Mills theory and mathematical ideas related to renormalization and the physics concept of dimensional transmutation.