Slides:

• Slides from my Invited Lecture on Monstrous Moonshine over the Integers, at the 2019 Japanese Mathematical Society Algebra Symposium.
• Slides from my Special Invited Lecture on recent progress in moonshine, at the 2017 Japanese Mathematical Society annual meeting.

GAP code for computing McKay-Thompson series and head character decompositions. McKay-Thompson series are the graded traces of elements of the monster acting on the monster vertex algebra. A head character decomposition is the decomposition of a graded piece of the monster vertex algebra into a direct sum of irreducible representations of the monster. Perhaps someday I will add something for computing Virasoro multiplicities.

Here are some old notes from my graduate school days:

• pdf Uncorrected notes from Borcherds' spring 2004 seminar on quantum field theory. 45pp
• pdf Borcherds' fall 2003 lectures on the lattice II_1,25. 10pp
• pdf 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