ICM 2022: Langlands Day

ICM 2022 is running virtually and you can already watch all the videos of past lectures at the IMU You-Tube channel, and probably even if you are not among the 7,000 registered participants you can see them “live” on You-Tube in the assigned date and hour. 

I landed back from Helsinki on Wednesday night and I devoted Thursday to watch lectures, while in later days other tasks and obligations gradually took over part of my time. I plan to catch up during the summer.

The three plenary lectures on Thursday, July 7 were around the Langlands program.

David Kazhdan, Marie-France Vignéras and Frank Calegari.

All three plenary lectures on Thursday were about the Langlands program. The opening lecture by my friend and colleague David Kazhdan proposed, mainly to experts in representation theory, a glance well beyond the horizon. David offered three complementary approaches to a far-reaching extension of the Langlands program where one attempts to replace “global fields” by more general fields. Specifically, David and his collaborators want to extend the unramified Langlands correspondence from fields of rational functions on curves over finite fields to fields of rational functions on curves over local fields. The ICM lecture was rather short, however, David gave two detailed talks at our basic notion seminar and here is the recording of the first lecture

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David Kazhdan’s lecture in our basic notion seminar

Marie-France Vignéras and Frank Calegari gave wonderful general audience lectures.  Marie-France even advised the experts in the lecture room to consider going somewhere else, and Frank posted his amazing mathematical video on his blog, adding a disclaimer that the target audience for his blog is close to orthogonal to the target audience for his talk. 

 

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Pictures from Calegari’s lecture: Some computations from Frank Calegari’s lecture may appeal to very large audiences (top left); Later things get more difficult: A recent breakthrough by Ana Caraiani and Peter Scholze (Caraiani also gave an ICM lecture) is mentioned and so is the recent proof of the Hasse-Weil conjecture for surfaces of genus 2!

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Pictures from Marie-France Vignéras’ lecture.

 

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