概要

顔写真 Name: Scott Carnahan
Affiliation: Faculty of Pure and Applied Sciences
Specialty: College of Mathematics
Field of Research:

Representation Theory

Position: Assistant Professor
Degree: Ph. D., Mathematics
Degree earning University : Department of Mathematics, University of California, Berkeley (May 2007)
Starting Date: November 16, 2012
Mentor: Professor Masahiko Miyamoto
Laboratory: http://www.math.tsukuba.ac.jp/~carnahan/

Generalized Moonshine

 The subject known as Monstrous Moonshine began in the 1970s, when numerical computations suggested a relationship between representations of the monster simple group and modular functions obeying a genus zero property.  The classical theories of modular functions on the complex upper half-plane and finite simple groups of symmetries were not previously thought to be closely related, and the initial observations were viewed with some skepticism.  However, Borcherds’s 1992 proof of the Monstrous Moonshine Conjecture, together with some preceding work, showed that ideas from theoretical physics, in particular conformal field theory, provide a bridge that links the two fields.  More recent work suggests that the mathematical objects that arise in moonshine are intimately related to the physics of black holes in the extreme quantum regime, where the mass takes the smallest possible nonzero value.
 My research is primarily concerned with the Generalized Moonshine Conjecture.  From a physical viewpoint, Borcherds’s theorem is concerned with the untwisted sector of an exceptional conformal field theory, while the general conjecture describes all twisted sectors.  By working on this question and related subjects, I hope to increase our understanding of both the mathematics and the fundamental physics that naturally appears in moonshine .