The work of Maryna Viazovska
Details
Speaker: Henry Cohn (Microsoft)
Home — Clay Research Conference — Page 4
Speaker: Henry Cohn (Microsoft)
Home — Clay Research Conference — Page 4
Speaker: Carlos Kenig (Chicago)
Home — Clay Research Conference — Page 4
Speaker: Tamar Ziegler (HUJ)
Home — Clay Research Conference — Page 4
Speaker: Ovidiu Savin (Columbia)
Home — Clay Research Conference — Page 4
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)
Home — Clay Research Conference — Page 4
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)
Home — Clay Research Conference — Page 4
We start with a classical problem of Kummer and Darboux about describing surfaces that contain many circles and explain an answer that uses polynomial solutions of quadratic forms over arbitrary fields.
Speaker: János Kollár (Princeton)
Home — Clay Research Conference — Page 4
Speaker: Bill Minicozzi (MIT)
Home — Clay Research Conference — Page 4
Speaker: Manjul Bhargava (Princeton)
Home — Clay Research Conference — Page 4
Abstract: Gauge theories are quantum field theories built directly out of local Lie group symmetry. Conversely, one can view many aspects of representation theory and harmonic analysis of Lie groups through the lens of gauge theory. We will explore the relation between centers and spectral decomposition in representation theory, on the one hand, and local operators and moduli spaces of vacua in gauge theory on the other (without assuming familiarity with either). Contemporary aspects of this relation featuring in the associated workshop include the interplay of geometric representation theory (in particular the geometric Langlands correspondence) with Seiberg-Witten geometry of supersymmetric gauge theories.
Speaker: David Ben-Zvi (UT, Austin)
Home — Clay Research Conference — Page 4
Speaker: Gil Kalai (HUJ)
Home — Clay Research Conference — Page 4
Speaker: Howard Masur (Chicago)