## 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.