# Difference between revisions of "Algebra and Algebraic Geometry Seminar Fall 2018"

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===Akhil Mathew=== | ===Akhil Mathew=== | ||

+ | |||

+ | '''Title: Kaledin's noncommutative degeneration theorem and topological | ||

+ | Hochschild homology''' | ||

+ | |||

+ | For a smooth proper variety over a field of characteristic | ||

+ | zero, the Hodge-to-de Rham spectral sequence (relating the cohomology | ||

+ | of differential forms to de Rham cohomology) is well-known to | ||

+ | degenerate, via Hodge theory. A "noncommutative" version of this | ||

+ | theorem has been proved by Kaledin for smooth proper dg categories | ||

+ | over a field of characteristic zero, based on the technique of | ||

+ | reduction mod p. I will describe a short proof of this theorem using | ||

+ | the theory of topological Hochschild homology, which provides a | ||

+ | canonical one-parameter deformation of Hochschild homology in | ||

+ | characteristic p. |

## Revision as of 13:22, 7 September 2018

The seminar meets on Fridays at 2:25 pm in room B235.

Here is the schedule for the previous semester.

## Contents

## Algebra and Algebraic Geometry Mailing List

- Please join the AGS Mailing List to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).

## Fall 2018 Schedule

date | speaker | title | host(s) |
---|---|---|---|

September 7 | Daniel Erman | Big Polynomial Rings | Local |

September 14 | Akhil Mathew (U Chicago) | TBA | Andrei |

September 21 | Andrei Caldararu | TBA | Local |

September 28 | Mark Walker (Nebraska) | TBD | Michael and Daniel |

October 5 | |||

October 12 | Jose Rodriguez (Wisconsin) | TBD | Local |

October 19 | Oleksandr Tsymbaliuk (Yale) | TBD | Paul Terwilliger |

October 26 | |||

November 2 | Behrouz Taji (Notre Dame) | TBD | Botong Wang |

November 9 | |||

November 16 | Wanlin Li | TBD | Local |

November 23 | Thanksgiving | No Seminar | |

November 30 | John Wiltshire-Gordon | TBD | Local |

December 7 | Michael Brown | TBD | Local |

December 14 |

## Abstracts

### Akhil Mathew

**Title: Kaledin's noncommutative degeneration theorem and topological**
Hochschild homology

For a smooth proper variety over a field of characteristic zero, the Hodge-to-de Rham spectral sequence (relating the cohomology of differential forms to de Rham cohomology) is well-known to degenerate, via Hodge theory. A "noncommutative" version of this theorem has been proved by Kaledin for smooth proper dg categories over a field of characteristic zero, based on the technique of reduction mod p. I will describe a short proof of this theorem using the theory of topological Hochschild homology, which provides a canonical one-parameter deformation of Hochschild homology in characteristic p.