Workshop on Dualisable Categories & Continuous $K$-theory

Mathew, Akhil and Scholze, Peter and Efimov, Alexander and Yakerson, Maria and Ramzi, Maxime (2024) Workshop on Dualisable Categories & Continuous $K$-theory. In: Workshop on Dualisable Categories & Continuous $K$-theory. (Unpublished)

[thumbnail of Workshop Program]
Preview
 Text (Workshop Program)
dualcat24-workshop-program.pdf - Supplemental Material
Download (93kB) | Preview
[thumbnail of Akhil Mathew, Introduction to dualisable categories and their $K$-theory, Part I] Video (Akhil Mathew, Introduction to dualisable categories and their $K$-theory, Part I)
Athil_Mathew_Part1_MQ.mp4 - Presentation
Download (668MB)
[thumbnail of Akhil Mathew, Introduction to dualisable categories and their $K$-theory, Part II] Video (Akhil Mathew, Introduction to dualisable categories and their $K$-theory, Part II)
Athil_Mathew_Part2_MQ.mp4 - Presentation
Download (703MB)
[thumbnail of Akhil Mathew, Introduction to dualisable categories and their $K$-theory, Part III] Video (Akhil Mathew, Introduction to dualisable categories and their $K$-theory, Part III)
Athil_Mathew_Part3_MQ.mp4 - Presentation
Download (739MB)
[thumbnail of Akhil Mathew, Introduction to dualisable categories and their $K$-theory, Part IV] Video (Akhil Mathew, Introduction to dualisable categories and their $K$-theory, Part IV)
Athil_Mathew_Part4_MQ.mp4 - Presentation
Download (606MB)
[thumbnail of Akhil Mathew, Introduction to dualisable categories and their $K$-theory, Part V] Video (Akhil Mathew, Introduction to dualisable categories and their $K$-theory, Part V)
Athil_Mathew_Part5_MQ.mp4 - Presentation
Download (699MB)
[thumbnail of Alexander Efimov, Dualizable categories and localizing motives, Part I] Video (Alexander Efimov, Dualizable categories and localizing motives, Part I)
Alexander_Efimov_Part1_MQ.mp4 - Presentation
Download (618MB)
[thumbnail of Alexander Efimov, Dualizable categories and localizing motives, Part II] Video (Alexander Efimov, Dualizable categories and localizing motives, Part II)
Alexander_Efimov_Part2_MQ.mp4 - Presentation
Download (557MB)
[thumbnail of Alexander Efimov, Dualizable categories and localizing motives, Part III] Video (Alexander Efimov, Dualizable categories and localizing motives, Part III)
Alexander_Efimov_Part3_MQ.mp4 - Presentation
Download (597MB)
[thumbnail of Alexander Efimov, Dualizable categories and localizing motives, Part IV] Video (Alexander Efimov, Dualizable categories and localizing motives, Part IV)
Alexander_Efimov_Part4_MQ.mp4 - Presentation
Download (564MB)
[thumbnail of Alexander Efimov, Dualizable categories and localizing motives, Part V] Video (Alexander Efimov, Dualizable categories and localizing motives, Part V)
Alexander_Efimov_Part5_MQ.mp4 - Presentation
Download (533MB)
[thumbnail of Exercises, Sep 12, 2024]
Preview
 Text (Exercises, Sep 12, 2024)
Exercises_for_the_workshop_on_dualisable_categories_and_continuous_K_theory.pdf - Supplemental Material
Download (466kB) | Preview
[thumbnail of Lecture notes by Akhil Mathew (texed by Chirantan Chowdhury)]
Preview
 Text (Lecture notes by Akhil Mathew (texed by Chirantan Chowdhury))
Lecture_Notes_from_Akhil_Mathew_texed_by_Chirantan_Chowdhury.pdf - Supplemental Material
Download (302kB) | Preview
[thumbnail of Peter Scholze, Refined $TC^{-}$ over perfectoid rings] Video (Peter Scholze, Refined $TC^{-}$ over perfectoid rings)
Peter_Scholze_Refined_TC-_MQ.mp4 - Presentation
Download (665MB)
[thumbnail of Maria Yakerson, Universality of algebraic $K$-theory] Video (Maria Yakerson, Universality of algebraic $K$-theory)
Maria_Yakerson_Universality_MQ.mp4 - Presentation
Download (667MB)
[thumbnail of Maxime Ramzi, Motives as a localization of categories] Video (Maxime Ramzi, Motives as a localization of categories)
Maxime_Ramzi_Motives_MQ.mp4 - Presentation
Download (645MB)

Abstract

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.

Item Type: Conference or Workshop Item (Lecture)
Subjects: 1 Discrete mathematics / algebra > 14-XX Algebraic geometry
1 Discrete mathematics / algebra > 19-XX K-theory
3 Geometry and topology > 55-XX Algebraic topology
Divisions: Research > Talks
Depositing User: This Admin
Date Deposited: 10 Sep 2024 12:12
Last Modified: 07 Oct 2024 11:32
URI: https://archive.mpim-bonn.mpg.de/id/eprint/5092

Actions (login required)

View Item View Item