Page 184 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 184
OPERATOR ALGEBRAS (MS-14)
C*-algebra of the monoid is generated by a family of isometries subject to an algebraic condi-
tion capturing the right LCM property. A choice of a monoid homomorphism into the positive
real numbers leads to a time evolution on the C*-algebra and a zeta function that records the
growth of the monoid elements. There is a generally rich structure of equilibrium states re-
flecting a fine interplay between critical values and values in an interval of convergence for this
series. Many authors have contributed to this development in recent years. In the talk I will
outline some key ideas and present the concrete case of Artin monoids, including the two large
classes of right-angled and finite-type monoids.
Rigidity of Roe algebras
Kang Li, kang.li@kuleuven.be
KU Leuven, Belgium
(Uniform) Roe algebras are C∗-algebras associated to metric spaces, which reflect coarse prop-
erties of the underlying metric spaces. It is well-known that if X and Y are coarsely equiv-
alent metric spaces with bounded geometry, then their (uniform) Roe algebras are (stably) ∗-
isomorphic. The rigidity problem refers to the converse implication. The first result in this
direction was provided by Ján Špakula and Rufus Willett, who showed that the rigidity problem
has a positive answer if the underlying metric spaces have Yu’s property A. I will in this talk
review all previously existing results in literature, and then report on the latest development in
the rigidity problem. This is joint work with Ján Špakula and Jiawen Zhang.
Cartan subalgebras in classifiable C*-algebras
Xin Li, xinli.math@gmail.com
University of Glasgow, United Kingdom
This talk is about Cartan subalgebras in classifiable C*-algebras. We will give an overview of
some recent results, including a general construction of Cartan subalgebras in all stably finite
classifiable C*-algebras and a detailed analysis of these Cartan subalgebras in example classes.
Boundary theory and amenability: from Furstenberg’s Poisson formula to
boundaries of Drinfeld doubles of quantum groups
Sergey Neshveyev, sergeyn@math.uio.no
University of Oslo, Norway
In his work on the Poisson formula for semisimple Lie groups Furstenberg attached two bound-
aries to every locally compact group G, which are now called the Poisson and Furstenberg
boundaries of G. As has been observed over the years, both constructions can be approached
from an operator algebraic point of view and extended to the noncommutative setting, leading
to the theories of noncommutative Poisson boundaries by Izumi and of injective envelopes by
Hamana. The noncommutative Poisson boundaries have been computed in a number of cases.
An important aspect of the computations, both in the classical and noncommutative settings,
182
C*-algebra of the monoid is generated by a family of isometries subject to an algebraic condi-
tion capturing the right LCM property. A choice of a monoid homomorphism into the positive
real numbers leads to a time evolution on the C*-algebra and a zeta function that records the
growth of the monoid elements. There is a generally rich structure of equilibrium states re-
flecting a fine interplay between critical values and values in an interval of convergence for this
series. Many authors have contributed to this development in recent years. In the talk I will
outline some key ideas and present the concrete case of Artin monoids, including the two large
classes of right-angled and finite-type monoids.
Rigidity of Roe algebras
Kang Li, kang.li@kuleuven.be
KU Leuven, Belgium
(Uniform) Roe algebras are C∗-algebras associated to metric spaces, which reflect coarse prop-
erties of the underlying metric spaces. It is well-known that if X and Y are coarsely equiv-
alent metric spaces with bounded geometry, then their (uniform) Roe algebras are (stably) ∗-
isomorphic. The rigidity problem refers to the converse implication. The first result in this
direction was provided by Ján Špakula and Rufus Willett, who showed that the rigidity problem
has a positive answer if the underlying metric spaces have Yu’s property A. I will in this talk
review all previously existing results in literature, and then report on the latest development in
the rigidity problem. This is joint work with Ján Špakula and Jiawen Zhang.
Cartan subalgebras in classifiable C*-algebras
Xin Li, xinli.math@gmail.com
University of Glasgow, United Kingdom
This talk is about Cartan subalgebras in classifiable C*-algebras. We will give an overview of
some recent results, including a general construction of Cartan subalgebras in all stably finite
classifiable C*-algebras and a detailed analysis of these Cartan subalgebras in example classes.
Boundary theory and amenability: from Furstenberg’s Poisson formula to
boundaries of Drinfeld doubles of quantum groups
Sergey Neshveyev, sergeyn@math.uio.no
University of Oslo, Norway
In his work on the Poisson formula for semisimple Lie groups Furstenberg attached two bound-
aries to every locally compact group G, which are now called the Poisson and Furstenberg
boundaries of G. As has been observed over the years, both constructions can be approached
from an operator algebraic point of view and extended to the noncommutative setting, leading
to the theories of noncommutative Poisson boundaries by Izumi and of injective envelopes by
Hamana. The noncommutative Poisson boundaries have been computed in a number of cases.
An important aspect of the computations, both in the classical and noncommutative settings,
182
