## Workshop on "Dualisable Categories & Continuous K-theory", September 9 - 13, 2024

Algebraic K-theory is an object that sits at the centre of large parts of algebra, geometry, and topology because of its universal role as a receptacle to count other mathematical objects with signs. However, since its invention, a phenomenon often called the Eilenberg swindle - which says that the algebraic K-theory of a category which is too large must necessarily be zero - has been accepted as a fundamental limit to the theory. Recently, Alexander Efimov introduced a construction called continuous K-theory which allows one to make sense of algebraic K-theory of certain large categories known as dualisable categories in a nontrivial way, thus surmounting the problem of the aforementioned Eilenberg swindle. These dualisable categories encompass geometrically interesting and previously inaccessible examples such as sheaves on locally compact Hausdorff spaces. This new direction in K-theory has seen many recent advancements such as the rigidity of non-commutative motives by Efimov and the polynomial functoriality of continuous K-theory by Akhil Mathew and collaborators.

In light of these developments, this workshop aims to bring the community of mathematicians in algebra, topology, and geometry up to speed on the latest results and perspectives spawned by the theory of dualisable categories and continuous K-theory. The workshop will consist of two main lecture series by Alexander Efimov and Akhil Mathew, augmented by multiple exercise sessions, which we hope will allow for the participants to obtain a working knowledge on the subject. There will also be research talks as well as a session of short contributed talks by participants.

**The main lecture series will be recorded and the recordings will be uploaded on the website. The talks will NOT be live streamed.**

**Main speakers:**

Alexander Efimov (Einstein Institute of Mathematics, Hebrew University of Jerusalem)

Akhil Mathew (University of Chicago)

**Speakers:**

Maxime Ramzi (University of Copenhagen)

Peter Scholze (MPIM Bonn)

Maria Yakerson (Oxford University)

### Registration

The registration is closed as of July 31, 2024.

### Contact:

dualcat2024$@$mpim-bonn$.$mpg$.$de

**Click here to watch recordings of the main lectures and talks.**

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Anhang | Größe |
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Exercises_for_the_workshop_on_dualisable_categories_and_continuous_K_theory.pdf | 455.72 KB |

Lecture_Notes_from_Akhil_Mathew_texed_by_Chirantan_Chowdhury.pdf | 295.08 KB |

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