The semester here is coming to a close. I’m way behind writing up notes for the lectures I’ve been giving, which are ending with covering the details of the Standard Model. This summer I’ll try to finish the notes and will be working on writing out explicitly the details of how the Standard Model works in the “right-handed” picture of the spinor geometry of spacetime that I outlined here.

At this point I need a vacation, heading soon to France for a couple weeks, then will return here and get back to work. There may be little to no blogging here for a while.

On the Langland’s front, Laurent Fargues is turning his Eilenberg lectures here last fall into a book, available here. In Bonn, Peter Scholze is running a seminar on Real local Langlands as geometric Langlands on the twistor-P1

**Update**: One more item. Videos of talks from a conference on arithmetic geometry in honor of Helene Esnault at the IHES last week are now available. Dustin Clausen’s talk covers one of my favorite topics (the Cartan model for equivariant cohomology), making use of the new formalism for handling he has developed with Scholze for handling C-infinity manifolds in a more algebraic way.

**Update**: Now back from vacation. While I was away, Quanta made up for its nonsense like this with a very nice article about “Weil’s Rosetta Stone” and what it has to do with geometric Langlands. In the comments people have pointed to the proof of geometric Langlands that has finally been finished, and New Scientist has an article (or see Edward Frenkel on Twitter here).

Peter,

I’m curious to know if there is a particular reason for which you’re always coming to France for vacation during the summer. Are other European countries, like Germany, Switzerland, Spain, Italy, or even Britain or Australia not interesting to you? Is it always Paris your destination here in France? Is there a math or physics conference you wish to attend here in France? Also, don’t you teach in the summer at your university? Do you have 3 months of vacation since the Fall semester there starts in September?

Best,

Bernard

Bernard l’Amateur,

I do travel a fair amount, for conferences or other reasons, have been to all the countries you mention in recent years, except Australia (have never been there, would very much like to go sometime). Paris is a favorite place to spend time in, for many reasons, including the fact that I partly grew up there. I usually don’t go there during the summer, since that’s when it’s hot, full of tourists and all the actual Parisians have left town. This year in particular there’s a very good reason not to be in Paris in the middle of the summer. This trip is not for a conference.

I don’t teach during the summer, but usually spend almost all of it in New York, which I enjoy, despite some periods when the heat/humidity is a bit much. It’s not vacation, I work on some combination of my own research or writing projects and dealing with tasks associated with the department computer system that I’m responsible for. Also, lots of long bike rides.

Hi Peter,

Your are saying: “…including the fact that I partly grew up there”. So are you fluent in french?

An update on the abc conjecture:

Kirti Joshi has posted two responses to Peter Scholze and Shinichi Mochizuki about their criticisms of Joshi’s proof of the abc conjecture: https://mathoverflow.net/a/470293

The documents can be found directly here:

https://www.math.arizona.edu/%7Ekirti/response-to-Mochizuki.pdf

https://www.math.arizona.edu/%7Ekirti/local-global-issue.pdf

The first document is directly addressed to Mochizuki himself, while the second document seems to be addressed to the general mathematical population.

Section 0.3 of the second document looks crucial in my eyes, since it highlights what Joshi thinks the flaw is exactly in the proof of Mochizuki’s original Corollary 3.12, and also in Joshi’s proof of Theorem 9.11.1, which is his version of Corollary 3.12. According to Joshi, Mochizuki’s proof of his Corollary 3.12 in IUT3 is incomplete because it relies upon Mochizuki’s Corollary 2.2 in IUT4 being proven first, but Mochizuki never proved Corollary 2.2 in IUT4 before proving Corollary 3.12 in IUT3 in his set of papers.

And as Joshi admits in the same section, he organized his Constructions papers in the same way that Mochizuki did, so that the two sets of abc papers can be compared. As a result, Joshi’s Theorem 9.11.1 in Constructions 3 relies on Theorem 5.7.1 in Constructions 4 to be proven first, but he put Theorem 5.7.1 after Theorem 9.11.1, so there is a gap in Joshi’s proof of Theorem 9.11.1.

What I’m not currently sure of is whether Joshi’s proof of Theorem 5.7.1 in Constructions 4 also relies on Theorem 9.11.1 in Constructions 3 (and similarly if Mochizuki’s Corollary 2.2 in IUT4 also relies on Corollary 3.12 in IUT3). If so, then there is a circular dependency which invalidates Joshi’s proof and Mochizuki’s original proof of the abc conjecture. If not, then Joshi should have valued logical correctness and logical completeness above following Mochizuki’s evidently poor organization of Mochizuki’s own proof outline, and put his proof of [Joshi’s] Theorem 5.7.1 in Constructions 4 before his Theorem 9.11.1 in Constructions 3, so as to bridge the gap that is currently in his proof of Theorem 9.11.1 in Constructions 3.

Good moment for a vacation; let’s hope that humidity will not damage Columbia in the next weeks.

Marvin,

My standard joke is that I speak French fluently but like a 12 year old (age when I came back to US).

Alessandro Strumia,

Yes, good timing for a vacation.

Last thing I want to do on my vacation (or ever) is host a discussion of this here. Last few months what I was seeing was often very different than what was on the internet and now I have no first hand information.

I’ve found the student run site bwog.com has quite complete and accurate reporting.

The first of a series of five papers claiming to prove geometric Langlands is on the arxiv.

Any reaction to the new proof of the geometric Langlands conjecture?

https://people.mpim-bonn.mpg.de/gaitsgde/GLC/

Sam Raskin gave two talks available on Youtube outlining the proof, which is many hundreds of pages. The papers include clarifications of folklore, and the precise setting for previous results, so it should be a great contribution both in content and in documentation. He says the Betti analog is more beautiful, if I recall, and that there is room for more understanding in the general case. The abstracts of the four draft papers are fun to read, with the middle paper still under re-organization (five papers total).

* Harvard CMSA, on April 9

* IAS, on May 6, announcing the actual proof

They are similar talks.

Peter, now that James Simons has died, would you consider writing up a brief blog entry on Chern-Simons theory and its potential role in quantizing gravity? This is, after all, JS’s greatest achievement–much greater than out-investing Buffet and Soros. Yet it’s almost impossible to explain. All the obits of Simons–like the ones today (5/11/24) on the front pages of the NY Times and the Wall St. Journal–allude to Chern-Simons in passing without further comment. I myself have a nugatory understanding of the theory, despite working through much of Baez & Muniain’s book on gauge fields, knots, and gravity. Please enlighten us!

Jim Holt,

On vacation without a keyboard so unable to do justice to Simons or Chern-Simons. Greetings from Montpellier!

I enthusiastically second Edward Frenkel’s suggestion (which might seem self-serving!) that a great place to learn how the Langlands program works is Frenkel’s own book “Love and Math.” His exposition of it there–especially geometric Langlands–is lively and quite beautiful.

Incidentally here is a short inquiry to provide one reason why Paris looks like a paradise for mathematic(ian)s

This is a list of cities with the largest number of winners of the Fields medal:

Paris, France – 12 winners

Princeton, United States – 7 winners

Moscow, Russia – 6 winners

Cambridge, United Kingdom – 5 winners

Zurich, Switzerland – 4 winners

Berkeley, United States – 3 winners

Göttingen, Germany – 3 winners

Harvard, United States – 3 laureates

Kyoto, Japan – 3 winners

Stanford, United States – 2 winners

Warning:

I asked Chat Mistral AI to make the list. E “counted the number of Fields Medal winners who were affiliated with an institution in each city at the time of their award. It is possible that errors or omissions were slipped”.

Data source: https://www.mathunion.org/imu-awards/fields-medal/laureates.