Chromatic Homotopy, K-Theory and Functors / Homotopie chromatique, K-théorie et foncteurs

Collection Chromatic Homotopy, K-Theory and Functors / Homotopie chromatique, K-théorie et foncteurs

Organizer(s) Ausoni, Christian ; Hess Bellwald, Kathryn ; Powell, Geoffrey ; Touzé, Antoine ; Vespa, Christine

Date(s) 23/01/2023 - 27/01/2023

linked URL https://conferences.cirm-math.fr/2339.html

00:00:00 / 00:00:00

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A survey of Mackey and Green 2-functors

By Ivo Dell'Ambrogio

Since the early 70s, Mackey and Green functors have been successfully used to model the induction and restriction maps which are ubiquitous in the representation theory of finite groups. In concrete examples, the latter maps are typically distilled, in some way, from induction and restriction functors between additive (abelian, triangulated...) categories. In order to better capture this richer layer of equivariant information with a (light!) set of axioms, we are naturally led to the notions of Mackey and Green 2-functors. Many such structures have been in use for a long time in algebra, geometry and topology. We survey examples and applications of this young—yet arguably overdue—theory. This is partially joint work with Paul Balmer and Jun Maillard.

Information about the video

Date of recording 23/01/2023
Date of publication 17/02/2023
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Jean Petit
Format MP4

Citation data

DOI 10.24350/CIRM.V.19996703
Cite this video Dell'Ambrogio, Ivo (23/01/2023). A survey of Mackey and Green 2-functors. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19996703
URL https://dx.doi.org/10.24350/CIRM.V.19996703

Domain(s)

Bibliography

BALMER, Paul et DELL'AMBROGIO, Ivo. Mackey 2-Functors and Mackey 2-Motives. 2020. - https://doi.org/10.4171/209
BALMER, Paul et DELL'AMBROGIO, Ivo. Green equivalences in equivariant mathematics. Mathematische Annalen, 2021, vol. 379, no 3-4, p. 1315-1342. - http://dx.doi.org/10.1007/s00208-021-02145-2
DELL'AMBROGIO, Ivo. Green 2-functors. Transactions of the American Mathematical Society, 2022, vol. 375, no 11, p. 7783-7829. - http://dx.doi.org/10.1090/tran/8681
MAILLARD, Jun. A categorification of the Cartan-Eilenberg formula. Advances in Mathematics, 2022, vol. 396, p. 108187. - https://doi.org/10.1016/j.aim.2022.108187

MSC codes

Document(s)

https://www.cirm-math.fr/RepOrga/2339/Slides/DellAmbrogio-ChroK.pdf

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