Duke

Workshop on Topological Dynamical Systems and Operator Algebras

University of Glasgow
December 2nd, 2016


Overview

This workshop will study connections between topological dynamical systems and operator algebras. The aim is to show how dynamical systems are studied through the lens of associated C*-algebras, which provide dynamical invariants in a noncommutative framework. The talks are meant to be introductory and we encourage postgraduates to attend.

The workshop will be complemented by a Scottish Operator Algebras Research Meeting on Saturday, December 3rd. Speakers and participants are strongly encouraged to attend both events.

Contact Mike Whittaker to register your attendance and please indicate if you wish to join us for dinner at Oran Mor.


Speakers

Nadia Larsen, University of Oslo
Xin Li, Queen Mary University of London
Mike Whittaker, University of Glasgow


Schedule (all talks in Mathematics 204)

- 12:30-1:20pm: Chris Heunen (part of SOAR Meeting)

Title: Functorial spectra and discretization of C*-algebras
Abstract: Much of the structure of a noncommutative C*-algebra is determined by the collection of its commutative C*-subalgebras. However, one can rigorously prove that it does not provide a full invariant. This question is answered by the notion of an active lattice, which adds the information of how different commutative C*-subalgebras relate to each other dynamically. After a survey of this area, I will discuss how one can reconstruct an AW*-algebra from its active lattice. Time permitting I will talk about extending this from AW*-algebras to C*-algebras, leading to so-called discretizations of a C*-algebra.

- 1:30-2:20pm: Nadia Larsen

Title: KMS states on right LCM semigroup C*-algebras
Abstract: C*-algebras that reflect algebraic structure of semigroups through families of isometries have been studied for a long time. In the past decade, motivated by examples arising in number theory, a general construction of C*-algebras associated to left cancellative semigroups was proposed by Li, and many new examples were found. Brownlowe, Ramagge, Robertson and Whittaker coined the notion of right LCM semigroup, and supplied large classes of examples by means of the Zappa-Szep product. One remarkable feature of C*-algebras that contain families of isometries is that they tend to admit "canonical" time evolutions and interesting structure of associated KMS, or equilibrium states. This has been the case for many classes of examples. Here we investigate the KMS state structure for natural dynamics in the general setup of the full C*-algebra of a right LCM semigroup. We identify internal structural properties of the semigroup, already predicted by the boundary quotient diagram of Stammeier, governing behaviour of the KMS states. This is joint work with Afsar, Brownlowe and Stammeier.

- 2:30-3pm: Coffee and tea

- 3:00-3:50pm: Xin Li

Title: Rigidity in C*-algebras and topological dynamics
Abstract: This talk is about Cartan subalgebras in C*-algebras and continuous orbit equivalence for topological dynamical systems. We explain how these notions build bridges between C*-algebras, topological dynamics, and geometric group theory. Moreover, we discuss rigidity phenomena in both settings.

- 4-5pm: Mike Whittaker

Title: KMS states on self-similar groupoid actions
Abstract: A self-similar groupoid action (G,E) consists of a faithful action of a groupoid G on the path space of a graph which displays a notion of self-similarity. In this talk I will explain this concept and construct a Cuntz-Pimsner algebra from (G,E). I will then consider KMS states associated with these C*-algebras. This talk is based on joint work with Marcelo Laca, Iain Raeburn, and Jacqui Ramagge.

- 5-6pm: Reception (Mathematics Common Room)

- 6:30-9pm: Dinner at Oran Mor.


Support

There is limited funds available for postgraduate students and postdocs. Please write to Mike Whittaker to apply for funding, the deadline to apply is November 1st. If you have been confirmed for funding, you have been booked into the Heritage Hotel (4-5 Alfred Terrace, Glasgow).


Travel to Glasgow

The PDF document "Getting to Glasgow Math School" provides comprehensive directions on getting here.


Funding

Funding for this meeting is provided by the London Mathematical Society through a Scheme 1 (new appointment) grant and by the University of Glasgow.


Participants

Rob Archbold (University of Aberdeen)
Jean Bellissard (Georgia Tech and the University of Münster)
Alexander Belton (Lancaster University)
Robbie Bickerton (Newcastle University)
Joan Bosa (University of Glasgow)
Sarah Browne (University of Sheffield)
Yemon Choi (Lancaster University)
Michael Dreher (Heriot-Watt University)
Sam Evington (University of Glasgow)
Ruaridh Gardner (University of Aberdeen)
Dimitrios Gerontogiannis (University of Glasgow)
Elizabeth Gillaspy (University of Münster)
Heiko Gimperlein (Heriot-Watt University)
Luke Hamblin (University of Glasgow)
Chris Heunen (University of Edinburgh)
Bence Horvath (University of Lancaster)
Evgenios Kakariadis (Newcastle University)
Nadia Larsen (University of Oslo)
Xin Li (Queen Mary University of London)
Ying-Fen Lin (Queen's University Belfast)
Andrew McKee (Queen's University Belfast)
Andrew Monk (University of Glasgow)
Ismail Ozkaraca (University of Glasgow)
Philip Scott (University of Ottawa)
Gábor Szabó (University of Aberdeen)
Aaron Tikuisis (University of Aberdeen)
Christian Voigt (University of Glasgow)
Simon Wassermann (University of Glasgow)
Stuart White (University of Glasgow)
Michael Whittaker (University of Glasgow)
Joachim Zacharias (University of Glasgow)