My Columbia colleague Patrick Gallagher passed away a few months ago at the age of 84. He had only recently retired, and for many years was the longest serving member of the department and an important part of its institutional memory. On October 10 there will be a memorial conference here at Columbia.
It’s too bad Pat didn’t live to see the latest from Terry Tao, who describes recent results which are related to old work of Gallagher’s by “Our proof of this theorem proceeds more or less along the same lines as Gallagher’s calculation, but now with k allowed to grow slowly with x.”
Turning to other topics, Peter Scholze continues to come up with new ideas about the foundations of mathematics at a pace far too fast for me to fool myself into thinking I might be able to follow what he’s doing. In recent months he has run a course on “Condensed Mathematics”, which involves new ideas about topology developed with Dustin Clausen. For a video of a recent talk where he explains this, see here.
On the Langlands/representation theory front, some interesting things are:
- A course run by Geordie Williamson in Sydney earlier this year.
- If you’re interested in what Williamson is up to, you might want to watch videos from “somewhere in Russia” last month, or “somewhere on Long Island” last week. Lecture notes are here.
- Also in Russia last month, at the Skoltech Center for Advanced Studies, where my Columbia colleague Igor Krichever is director, there was a skoltech summer school on mathematical physics, with some of the lectures on video here.
- Several new papers addressing different points of view about geometric Langlands are out, including a very recent one from Etingof, Frenkel and Kazhdan. For some background on the relation of this to work by Langlands himself, see here and here. For some geometric Langlands-related work of a different sort, see here and here.
Finally, the 2019 PCMI was devoted to the topic of Quantum Field Theory and Manifold Invariants, videos are here.
Update: Also on the Langlands/representation theory/quantum front, this week at Northeastern there’s a conference going on (rumored to be celebrating the fact that Etingof and Okounkov share the same birthday, and are now 50). Videos are starting to appear here, including one of Edward Frenkel discussing the paper with Etingof and Kazhdan mentioned above.