# 2019 Workshop

## Algebraic K-Theory with Benjamin Antieau and David Gepner

July 7 - 13, 2019

Rheinböllen, Germany

Participants of the 2019 workshop

### About

The fifth European Talbot workshop will take place in Germany July 7 - 13, 2019. The goal is to bring together a group of 30-35 graduate students and post-docs to work on a focused topic under the guidance of two senior mentors.

Most of the talks were given by the participants, with enough free time in the afternoon and evenings for further discussions and interaction. The character of the workshop is expository in nature, starting with the basic ideas and leading to a survey of the most recent developments in the field. Since all participants are staying together at a group house, jointly responsible for cooking and cleaning, we hope to create an informal and inspiring atmosphere.

### Topic

Algebraic K-theory is an exciting and interconnected area of mathematics intersecting geometry, topology, and number theory. The subject has proven extremely fruitful; as a cohomology theory, algebraic K-theory carries a significant amount of arithmetic information about the mathematical objects it is applied to. Unfortunately, algebraic K-theory groups are notoriously difficult to compute; for example, we have yet to see a full computation of the K-groups of the integers. However, recent years has seen exciting new progress within the subject of algebraic K-theory using the language of infinity-categories as developed by Lurie and Joyal. In this workshop we will approach algebraic K-theory from the perspective of algebraic topology and algebraic geometry, with some discussion on the interplay between algebraic K-theory and topological Hochschild homology.

The goal is to cover a good part of the background on algebraic K-theory, using modern language, reaching to some of the most recent papers on the topic like:

*Algebraic K-theory and descent for blow-ups*by Moritz Kerz, Florian Strunk, and Georg Tamme.*Excision in algebraic K-theory revisited*by Georg Tamme.*On the K-theory of pullbacks*by Markus Land and Georg Tamme.*On the Dundas-Goodwillie-McCarthy theorem*by Sam Raskin.*K-theory and topological cyclic homology of Henselian pairs*by Dustin Clausen, Akhil Mathew, and Matthew Morrow.*Descent in algebraic K-theory and a conjecture of Ausoni-Rognes*by Dustin Clausen, Akhil Mathew, Niko Naumann, and Justin Noel.

### Application

The application deadline has now passed.

### Poster

The poster for the workshop may be found here.

### Funding

The local expenses for all participants will be covered by the workshop, in particular costs for accommodation and meals. Additional funds covering travel expenses might become available, however we strongly encourage participants to look for funding themselves.

### Notes

Here are the notes from the workshop. These were originally live-TeXed by Lucy Yang and Jack Davies.

### Contact

For questions or suggestions, please send an email to the organisers at organisers@europeantalbot.org.

This workshop is organised by Bertram Arnold, Luci Bonatto, Jack Davies, and Alice Hedenlund, with coordinator (SFB contact) Georgios Raptis. We gratefully acknowledge funding and support from SPP 1786 and SFB 1085.