# MATH Seminar

Title: A Borcherds-Kac-Moody Superalgebra with Conway symmetry
Seminar: Algebra
Speaker: Natalie Paquette of Caltech
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2018-11-27 at 4:00PM
Venue: MSC W301
Abstract:
We construct a Borcherds-Kac-Moody superalgebra on which the Conway group $Co_0$ acts faithfully. We show that this algebra is generated by vertex operators, or "BRST-closed" states, in a chiral superstring theory. This parallels the construction of the Monster Lie algebra by Borcherds. We use this construction to produce denominator identities for the partition functions/McKay Thompson series of the vertex operator algebra known as the Conway module $V^{s \natural}$, described by Frenkel-Lepowsky-Meurman and Duncan. This work is in collaboration with S. Harrison and R. Volpato. If time permits, we explain how this construction may be promoted to a full (non-chiral) string theory compactification, following related work on Monstrous moonshine and string theory in collaboration with D. Persson and R. Volpato.