Talk notes and slides


Selected notes for research talks

Before giving a talk, I usually make an electronic handwritten version of my notes -- I am making a selection of these notes, which may be of general interest, available.

For general audiences

Every once in a while, I'll give a talk to high school students or undergraduates (and once or twice to more general audiences).  Below are some notes and slides from such talks.

  • Graphs and representation theory -- a talk using Lie algebra representation theory to prove some facts from graph theory. The talk is aimed at undergraduate math majors.
  • The music of the spheres -- a talk about the history of (mostly incorrect) theories of cosmology, from Pythagoras to Kepler.  Largely inspired by Arthur Koestler's The Sleepwalkers.
  • Tiling problems -- a talk about tiling problems (feasibility, counting, etc.) aimed at an undergraduate audience.
  • Zeroes of integer linear linear recurrences -- a talk about the Mahler-Skolem-Lech theorem, characterizing the possible zero sets of integer linear recurrences; includes a baby introduction to p-adic analysis.  The talk is aimed at undergraduate math majors.

Selected Older notes

Here are some old notes which might be useful.

  • Motivic analytic number theory -- a talk about some of my work on the Grothendieck ring of varieties.
  • The cotangent complex -- expository notes from a talk on the cotangent complex from a seminar at Stanford about perfectoid spaces.
  • The fundamental group and polylogarithms -- notes from an expository talk at Columbia, about Deligne's paper on the fundamental group of the projective line with three points removed.
  • The pairing on the Brauer group -- notes from an expository talk on the pairing on the l-power torsion in the Brauer group of a surface over a finite field, following Tate.  The talk was for a seminar at Columbia.


Here are some notes to myself about things I thought about a while ago, and notes other people have taken on casual talks I've given.

  • Homotopical enhancements of cycle class maps -- at some point I thought about enhancing the cycle class maps to intermediate Jacobians to fancier gadgets (maps to higher analytic stacks).  I think there are some intriguing heuristics that suggest such constructions might be useful, but I was never able to make anything work.  These notes are not written in a rigorous way, so let me know if you have questions about how to make things rigorous.
  • Sam Nolen took some notes on two talks I gave a while ago:  Here are notes on a talk I gave on some ideas related to Verdier duality and scanning in algebraic topology (the document also contains notes on a nice talk by Arnav Tripathy).  And here are some notes on a talk I gave about "motivic analytic number theory" on a decommissioned icebreaker in the San Francisco bay (the document also contains notes on a nice talk by Jeremy Booher on the Weil conjectures and on Serre's Kahler analogue thereof).