J. F. Duncan

Me

John F. Duncan

Harvard University
Department of Mathematics
One Oxford Street
Cambridge, MA 02138
U.S.A.
Office:
Phone:
Web:
Email: 		SC 320
(617) 495 5377
math.harvard.edu/~jfd/
duncan (at) math
Page last revised:
March 19th, 2008

Homepage

About me

I am a Benjamin Peirce Lecturer on Mathematics in the Department of Mathematics at Harvard University. I work on the representation theory of vertex algebras, and the connections between this and other fields, such as group theory, number theory, and algebraic geometry.

My curriculum vitae is available here in PDF, and here in DVI.

Teaching

I will be instructing the Spring 2008 offering of Mathematics 137: Algebraic Geometry, at Harvard University. This course is an introduction to the basic notions of algebraic geometry, with a particular focus on complex algebraic curves.

Mathematics 137 webpages:

Publications

I have three papers available on the arXiv:
math.RT/0502267 Super-moonshine for Conway's largest sporadic group.
The subject of this article is the unique self-dual N=1 super vertex operator algebra of rank 12 with no short elements. We prove that the full symmetry group of this object is the largest sporadic simple group of Conway. (We also explain what we mean by "N=1 super vertex operator algebra" and "no short elements", and we prove the uniqueness.)
math.RT/0609449 Moonshine for Rudvalis's sporadic group I.
We introduce the notion of enhanced vertex operator superalgebra (enhanced VOA) and construct an example that is self-dual, and whose full automorphism group is the direct product of a group of order seven with the sporadic simple group of Rudvalis. This is significant since the Rudvalis group is one of the sporadic groups that is not involved in the Monster, and we thus obtain a non-Monstrous analogue of Monstrous Moonshine via the characters associated to the Rudvalis group action on this infinite dimensional module.
math.RT/0611355 Moonshine for Rudvalis's sporadic group II.
We construct a second example of an enhanced vertex operator superalgebra that is self-dual, and whose full automorphism group is a cyclic cover of the sporadic simple group of Rudvalis. We observe that the series associated to the Rudvalis group via its action on the enhanced vertex algebras defined here and in Part I satisfy a genus zero property.