# Algebra and Algebraic Geometry Seminar Spring 2018

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

Here is the schedule for the previous semester.

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

TBA

TBA