Scott Carnahan

Scott Carnahan Address: University of Tsukuba Office: Science Building B, room 816 Email: still being set up IPMU location: A48

I study representation theory, with some emphasis on low-dimensional physics and arithmetic. My primary project concerns monstrous moonshine, and this involves some work with infinite dimensional Lie algebras, vertex algebras, algebraic curves, and automorphic functions. I am working on additional projects in chiral algebras and nonarchimedean geometry, but they are somewhat less developed.

Slides:

Slides from my talk on singular commutative rings at the ICMS workshop, on September 1, 2009. It may be a bit difficult to read, since it was aimed at vertex algebra specialists.

Old teaching and seminar materials:

For the spring 2010 term, I taught 18.784, seminar in number theory at MIT. It was aimed at advanced undergraduates in mathematics, and focused on modular forms.
For the spring 2009 term, I taught 18.086, Mathematical methods for Engineers II, at MIT. It was aimed at graduate students in engineering, and focused on PDE initial value problems, large linear systems, and optimization.
During the spring 2008 semester, I co-organized the pre-Talbot seminar with John Francis, at MIT. The topic was geometric Satake correspondence for quantum groups

Here are some old notes:

dvi.gz pdf ps.gz Notes from Borcherds' spring 2004 seminar on quantum field theory (very much out of date - additional info) 45pp
dvi.gz pdf ps.gz Borcherds' fall 2003 lectures on the lattice II_1,25. 10pp
dvi.gz pdf ps.gz Notes from Cheewhye Chin's seminar on Langlands correspondence for GL_r over function fields, 2002-2003. 135 pp
pdf Notes on the geometric Langlands program, from Talbot 2005. Megumi Harada scanned 81 pages of her notes, and I added one of mine (the ugly one). 10MB
I. M. Gelfand, D. A. Kazhdan, Some problems of differential geometry and the calculation of cohomologies of Lie algebras of vector fields, Soviet Math Dokl. 12 (1971) no. 5 1367-1371. I typed this up because it was nearly impossible to find.