Page 181 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
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OPERATOR ALGEBRAS (MS-14)
Nuclear Dimension of Simple C*-Algebras and Extensions
Samuel Evington, samuel.evington@maths.ox.ac.uk
University of Oxford, United Kingdom
The nuclear dimension of a C*-algebra, introduced by Winter and Zacharias, is a non-commu-
tative generalisation of the covering dimension of a topological space.
Whilst any non-negative integer or infinity can be realised as the nuclear dimension of some
commutative C*-algebra, the nuclear dimension of a simple C*-algebra must be either 0,1 or
infinity. This trichotomy is just one application of my joint work on the Toms–Winter Conjec-
ture with Castillejos, Tikuisis, White, and Winter. In this talk, I will outline the results, their
application to classification theory, and the new ideas at the heart of our work.
I will then discuss the recent developments on the nuclear dimension of extensions, includ-
ing the work on the Cuntz–Toeplitz algebras undertaken during the Glasgow Summer Project
2019.
Quantum groups in the heat
Amaury Freslon, amaury.freslon@math.u-psud.fr
Université Paris-Saclay, France
Coauthors: Lucas Teyssier, Simeng Wang
In this talk, I will consider the diffusion of the heat semi-group on free orthogonal quantum
groups. In the case of classical orthogonal groups, this is the Markov semi-group associated
to the Brownian motion, and it is known to spread very abruptly in the sense that it exhibits a
cut-off phenomenon (this is a result of P.-L. Meliot).
I will explain what this means and show that this phenomenon also occurs in the quantum
setting. I will further detail how one can get a more precise description of the behaviour of the
semi-group around the mixing time by computing the so-called limiting profile. This is based
on a joint work with L. Teyssier and S. Wang.
Nuclear dimension of crossed products attached to partial
homeomorphisms
Shirly Geffen, shirlygeffen@gmail.com
Ben Gurion University of the Negev, Israel, and WWU Münster, Germany
The concept of a C*-algebraic partial automorphism, namely an isomorphism between two ide-
als of a C*-algebra, was introduced by Exel in the 1990s. Many important C*-algebras that can-
not be written as a crossed product by a (global) automorphism, have a description as a crossed
product by a partial automorphism. In connection with the classification program, I show that in
some cases crossed products attached to partial homeomorphisms on finite-dimensional spaces,
have finite nuclear dimension.
179
Nuclear Dimension of Simple C*-Algebras and Extensions
Samuel Evington, samuel.evington@maths.ox.ac.uk
University of Oxford, United Kingdom
The nuclear dimension of a C*-algebra, introduced by Winter and Zacharias, is a non-commu-
tative generalisation of the covering dimension of a topological space.
Whilst any non-negative integer or infinity can be realised as the nuclear dimension of some
commutative C*-algebra, the nuclear dimension of a simple C*-algebra must be either 0,1 or
infinity. This trichotomy is just one application of my joint work on the Toms–Winter Conjec-
ture with Castillejos, Tikuisis, White, and Winter. In this talk, I will outline the results, their
application to classification theory, and the new ideas at the heart of our work.
I will then discuss the recent developments on the nuclear dimension of extensions, includ-
ing the work on the Cuntz–Toeplitz algebras undertaken during the Glasgow Summer Project
2019.
Quantum groups in the heat
Amaury Freslon, amaury.freslon@math.u-psud.fr
Université Paris-Saclay, France
Coauthors: Lucas Teyssier, Simeng Wang
In this talk, I will consider the diffusion of the heat semi-group on free orthogonal quantum
groups. In the case of classical orthogonal groups, this is the Markov semi-group associated
to the Brownian motion, and it is known to spread very abruptly in the sense that it exhibits a
cut-off phenomenon (this is a result of P.-L. Meliot).
I will explain what this means and show that this phenomenon also occurs in the quantum
setting. I will further detail how one can get a more precise description of the behaviour of the
semi-group around the mixing time by computing the so-called limiting profile. This is based
on a joint work with L. Teyssier and S. Wang.
Nuclear dimension of crossed products attached to partial
homeomorphisms
Shirly Geffen, shirlygeffen@gmail.com
Ben Gurion University of the Negev, Israel, and WWU Münster, Germany
The concept of a C*-algebraic partial automorphism, namely an isomorphism between two ide-
als of a C*-algebra, was introduced by Exel in the 1990s. Many important C*-algebras that can-
not be written as a crossed product by a (global) automorphism, have a description as a crossed
product by a partial automorphism. In connection with the classification program, I show that in
some cases crossed products attached to partial homeomorphisms on finite-dimensional spaces,
have finite nuclear dimension.
179
