# Algebra and Algebraic Geometry Seminar Spring 2018

The seminar meets on Fridays at 2:25 pm in room B113.

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).

## Spring 2018 Schedule

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

January 26 | Tasos Moulinos (UIC) | Derived Azumaya Algebras and Twisted K-theory | Michael |

February 2 | Daniel Erman (Wisconsin) | TBA | Local |

February 8 (unusual date!) | Roman Fedorov (University of Pittsburgh) | TBA | Dima |

February 9 | Juliette Bruce (Wisconsin) | TBA | Local |

February 23 | Aron Heleodoro (Northwestern) | TBA | Dima |

April 6 | Phil Tosteson (Michigan) | TBA | Steven |

April 13 | Reserved | Daniel | |

April 20 | Alena Pirutka (NYU) | TBA | Jordan |

April 27 | Alexander Yom Din (Caltech) | TBA | Dima |

May 4 | John Lesieutre (UIC) | TBA | Daniel |

## Abstracts

### Tasos Moulinos

**Derived Azumaya Algebras and Twisted K-theory**

Topological K-theory of dg-categories is a localizing invariant of dg-categories over [math] \mathbb{C} [/math] taking values in the [math] \infty [/math]-category of [math] KU [/math]-modules. In this talk I describe a relative version of this construction; namely for [math]X[/math] a quasi-compact, quasi-separated [math] \mathbb{C} [/math]-scheme I construct a functor valued in the [math] \infty [/math]-category of sheaves of spectra on [math] X(\mathbb{C}) [/math], the complex points of [math]X[/math]. For inputs of the form [math]\operatorname{Perf}(X, A)[/math] where [math]A[/math] is an Azumaya algebra over [math]X[/math], I characterize the values of this functor in terms of the twisted topological K-theory of [math] X(\mathbb{C}) [/math]. From this I deduce a certain decomposition, for [math] X [/math] a finite CW-complex equipped with a bundle [math] P [/math] of projective spaces over [math] X [/math], of [math] KU(P) [/math] in terms of the twisted topological K-theory of [math] X [/math] ; this is a topological analogue of a result of Quillen’s on the algebraic K-theory of Severi-Brauer schemes.

### Aron Heleodoro

**TBA**

### Alexander Yom Din

**TBA**