I warmly invite you to attend the following short course:
Title: Noncommutative Hodge-to-de Rham degeneration.
Speaker: Dmitry Kaledin (Steklov Institute).
Abstract: I am going to give an overview of the proof of what is known as "non-commutative Hodge-to-de Rham Degeneration Theorem": for any smooth and proper DG algebra over a field of characteristic 0, the Hochschild-to-cyclic spectral sequence degenerates at first term.
Dates: 7, 14 and 21 of May 2021 (Fridays) at 14:00-15:00 (GMT time).
Link: To appear soon. This event is open to all and will be streamed on Microsoft Teams.
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