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Noncommutative Hodge-to-de Rham degeneration

I warmly invite you to attend the following short course:


Title: Noncommutative Hodge-to-de Rham degeneration.

Speaker: Dmitry Kaledin (Steklov Institute).

Link: zoom.us/j/2667953619. This event is open to all and will be streamed on Zoom.


Lecture I: Non-commutative Hodge-to-de Rham Degeneration I.

Date: 7 May 2021 (Friday) at 14:00-15:00 (London time).

Abstract: I am going to review the usual commutative Hodge-to-de Rham Degeneration and its proofs, especially the proof by reduction to positive characteristic discovered by Deligne and Illusie. Then I will state the non-commutative counterpart of the main theorem.

Video: http://bogomolov-lab.ru/video/l-1.mp4


Lecture II: Non-commutative Hodge-to-de Rham Degeneration II.

Date: 14 May 2021 (Friday) at 14:00-15:00 (London time).

Abstract: I am going to explain the main ingredients that go into the non-commutative version of the method of Deligne-Illusie (in particular, co-periodic cyclic homology and the conjugate spectral sequence).

Video: http://bogomolov-lab.ru/video/l-2.mp4


Lecture III: Non-commutative Hodge-to-de Rham Degeneration III.

Date: 21 May 2021 (Friday) at 14:00-15:00 (London time).

Abstract: I am going to prove the theorem, and then explain some of its wider ramifications and possible generalizations. If time permits, I will also touch on its relation to stable homotopy theory and Topological Hochschild Homology.

Video: http://bogomolov-lab.ru/video/l-3.mp4


Historical context (written by the organizer): In the eighties, Deligne and Illusie (following earlier work of Faltings), gave a purely algebraic proof of the degeneration of the classical Hodge-to-de Rham spectral sequence. Later, in the 00’s, Kontsevich and Soibelman conjectured that the noncommutative Hodge-to-de Rham spectral sequence (where smooth proper algebraic varieties are replaced by smooth proper dg algebras) should also degenerate. Recently, Kaledin proved Kontsevich-Soibelman’s conjecture. Kaledin’s proof makes use of several different tools from algebra, algebraic geometry, representation theory and algebraic topology. Therefore, I believe this short course to be of interest to a broad mathematical audience.


Organizer: Goncalo Tabuada