The Fuglede-Kadison determinant of matrix-valued semicircular elements and the noncommutative Edmonds' problem | Vidéo | Carmin.tv

00:00:00 / 00:00:00

The Fuglede-Kadison determinant of matrix-valued semicircular elements and the noncommutative Edmonds' problem

Apparaît dans la collection : Chaire Jean Morlet - Conference - Algebraic aspects of random matrices / Chaire Jean Morlet - Conference - Aspects algébriques des matrices aléatoires

Over the last couple of years, it has become evident that matrix-valued semicircular elements establish strong links between free probability theory and noncommutative algebra. Another surprising connection of this kind was found in a recently finished project with Roland Speicher. We have shown that the Fuglede-Kadison determinant of an arbitrary matrix-valued semicircular element is essentially given by the capacity of its associated covariance map. In addition, we have improved a lower bound by Garg, Gurvits, Oliveira, and Widgerson on this capacity, by making it dimension-independent. Besides analytic tools from operator-valued free probability, these are the crucial ingredients in some novel algorithmic solution to the noncommutative Edmonds' problem which we described in collaboration with Johannes Hoffmann. In my talk, I will present our work and provide the background on free probability and noncommutative algebra required for this purpose.

Informations sur la vidéo

Date de captation 07/10/2024
Date de publication 04/11/2024
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Luca Recanzone
Format MP4

Données de citation

DOI 10.24350/CIRM.V.20255503
Citer cette vidéo Mai, Tobias (07/10/2024). The Fuglede-Kadison determinant of matrix-valued semicircular elements and the noncommutative Edmonds' problem. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20255503
URL https://dx.doi.org/10.24350/CIRM.V.20255503

Domaine(s)

Bibliographie

HOFFMANN, Johannes, MAI, Tobias, et SPEICHER, Roland. Computing the noncommutative inner rank by means of operator-valued free probability theory. arXiv preprint arXiv:2308.03667, 2023. - https://doi.org/10.48550/arXiv.2308.03667
MAI, Tobias et SPEICHER, Roland. Fuglede-Kadison determinants of matrix-valued semicircular elements and capacity estimates. arXiv preprint arXiv:2406.15922, 2024. - https://doi.org/10.48550/arXiv.2406.15922

Codes MSC

Dernières questions liées sur MathOverflow

Pour poser une question, votre compte Carmin.tv doit être connecté à mathoverflow

Poser une question sur MathOverflow

Copyright Carmin.tv 2026

Donner son avis