Finite groups via infinite Lie algebra

John Duncan, Harvard University

Finite groups are, generally speaking, extremely complicated. Surprisingly, there are some naturally arising (yet infinite dimensional) Lie algebras that seem to ``know'' certain finite groups, when viewed in an appropriate context. This hints at a Lie algebraic approach to the study of these groups. We survey some aspects of this approach, pointing out applications to sporadic groups, and connections with other fields, along the way.

John Duncan was born and raised in Wellington, New Zealand. He completed Bachelor's and Master's degrees at Auckland University (also in New Zealand), before entering graduate school in Mathematics at Yale University in the Fall of 2000. John completed his degree under the supervision of Igor Frenkel in May of 2006, and has been a Benjamin Pierce Instructor at Harvard University since the Fall of 2006. Present research interests include: the structure theory of vertex algebras, and applications of vertex algebra in representation theory, algebraic geometry, number theory, and topology.