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.
- 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.

Here are some old notes:

- 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