p-adic geometry
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Speaker: Peter Scholze (Bonn)
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Speaker: Peter Scholze (Bonn)
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Speaker: Ngô Bao Châu (Chicago)
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Speaker: Andrew Wiles (Oxford)
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Speaker: Claire Voisin (Collège de France)
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Speaker: Ben Green (Oxford)
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Correction: the work cited at 1:02:30 is of Richard Bamler.
Speaker: John Morgan (Stony Brook)
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Speaker: Henry Cohn (Microsoft)
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Speaker: Carlos Kenig (Chicago)
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Speaker: Tamar Ziegler (HUJ)
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Speaker: Ovidiu Savin (Columbia)
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Abstract: In this talk I will present an approach to non-commutative algebraic geometry based on the following principle: a non-commutative variety simply is a category. This principle seems naive at first sight, but it has been very fruitful during the last 20 years, thanks to the works of many authors such as Kapranov, Bondal-Orlov, Rosenberg, Van den Bergh, Artin-Zhang, Konstevich-Soibelman, Keller, etc.
The purpose of this lecture is to explain how we can (or can not) “do geometry” with categories with a particular focus on cohomological and numerical aspects: Euler characteristic, Lefschetz’s type trace formula, etc. I will illustrate this by exploring its interactions with singularity theories, both in the classical complex analytic situation and in more arithmetic settings. In the last part of the lecture I will explain how this approach to non-commutative geometry can be used in order to make progress on the, still conjectural, Bloch’s conductor formula.
Speaker: Bertrand Toën (Toulouse)
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Abstract: In the last few years, Jean Bourgain and Ciprian Demeter have proven a variety of striking “decoupling” theorems in Fourier analysis. The method has applications both in PDE and in number theory. In particular, it resolved a question about diophantine equations raised by Vinogradov in the 1930s.
The proof of decoupling uses geometric ideas. In particular, it gets a lot of mileage out of studying the problem at many different scales.
In this lecture, I will introduce decoupling and explain how it connects to number theory, and then I will sketch some of the ideas of the proof.
Speaker: Larry Guth (MIT)