Algebra, Geometry and C*-algebras

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Algebra, Geometry and C*-algebras

 19 - 23 Jun 2023

ICMS, Bayes Centre, Edinburgh


Scientific Organisers

  • Nadia Larsen, University of Oslo
  • Mark V Lawson, Heriot-Watt University
  • Aidan Sims, University of Wollongong
  • Alina Vdovina, CUNY
  • Mike Whittaker, University of Glasgow


Following the  success of the Higher Rank Graphs workshop in 2019 it was suggested to the organisers that they explore the broader connections between C*-algebras and the rest of mathematics and not restrict their focus to those C*-algebras that happen to arise from higher rank graphs. There are good reasons for doing this. Operator algebras in general have been influential on mathematics at least since the pioneering work of Marshall Stone in the 1930's. While C*-algebras interact nicely with many other areas of mathematics, the majority of work has been to bring outside ideas into the C*-algebraic framework. However, there are rare but significant advances in the other direction; for example, the Jones polynomial in knot theory, Alain Connes' non-commutative geometry program, and Krieger's invariant for subshifts of finite type. Many important connections between C*-algebras and the rest of mathematics are mediated by etale groupoids which connect the theory of C*-algebras with group theory advanced aspects of category theory such as the theory of toposes (via etendues). There are also important connections between the theory of C*-algebras and the theory of algebras in general such as Leavitt path algebras and Steinberg algebras and algebras that arise naturally in theoretical physics.

This workshop therefore aimed to bring together experts in the theory of C*-algebras with mathematicians who have already been inspired by C*-algebras or who work in areas where there are natural connections with C*-algebras.


Monday 19 June 2023
Welcome by Nadia Larsen & Housekeeping by ICMS
Sessions chaired by Nadia Larsen
Aidan Sims, University of Wollongong Groupoids from the C*-algebraic perspective
Morning tea
Richard Garner, Macquarie University Universal algebra and operator algebra
Sessions chaired by Mike Whittaker
Becky Armstrong , University of Münster Conjugacy of local homeomorphisms via groupoids and C*-algebras
Brita Nucinkis , Royal Holloway, University of London On generalisations of Thompson’s group V
Afternoon tea
Kevin Aguyar Brix , University of Glasgow Ideal structure of C*-algebras from dynamics
Drinks reception
Tuesday 20 June 2023
Sessions chaired by Ganna Kudryavtseva
Lisa O. Clark , Victoria University of Wellington Groupoids in analysis and algebra
Alejandra Garrido Angulo , Universidad Complutense de Madrid Topological Boolean inverse monoids
Morning tea
James Belk , University of Glasgow Embeddings into Topological Full Groups
Sessions chaired by Gwion Evans
Francesca Arici , Universiteit Leiden Spheres, Euler classes and the K-theory of C*-algebras of subproduct systems
Tristan Bice , Institute of Mathematics of the Czech Academy of Sciences in Prague Lawson-Pierce Duality
Afternoon tea
Benjamin Steinberg , CUNY Simplicity of inverse semigroup and etale groupoid algebras
Public lecture given by Brita Nucinkis and chaired by Alina Vdovina Paradoxical decompositions, amenable groups, and a chameleon
Wednesday 21 June 2023
Sessions chaired by Jeff Boersema
Jack Spielberg , Arizona State University From left cancellative small categories to C*-algebras, with examples
Victoria Gould , University of York Right ideal Howson semigroups and coherency
Morning tea
Yuhei Suzuki , Hokkaido University Amenable actions on finite simple C*-algebras arising from flows on pimsner algebras
Lunch / Group picture
Thursday 22 June 2023
Sessions chaired by Ying-Fen Lin
Enrique Pardo , Universidad de Cadiz Refinement monoids: a survey
Malcolm Jones, Victoria University of Wellington, New Zealand Groupoids of non-finitely aligned higher-rank graphs
Jeremy Brent Hume, University of Glasgow The K-theory of a rational function
Morning tea
Chris Heunen , University of Edinburgh Categories like Hilbert spaces
Sessions chaired by Nathan Brownlowe
Fabienne Chouraqui , University of Haifa Connections between the Yang-Baxter equation and Thompson's group F
Jamie Gabe , University of Southern Denmark Invariants for inclusions of C*-algebras
Afternoon tea
Chris Bruce , University of Glasgow From algebraic actions to C*-algebras and back again
David Pask, University of Wollongong Higher rank graphs, a brief survey
Friday 23 June 2023
Sessions chaired by Mark V Lawson
Elizabeth Gillaspy , University of Montana Williams' conjecture holds for meteor graphs
Camila F. Sehnem , University of Waterloo C*-envelopes of tensor algebras of product systems
Morning tea
Alina Vdovina , CUNY Higher structures in Algebra, Geometry and C*-algebras
Sessions chaired by Mark V Lawson, Supernumerary talks:
Nora Szakacs , University of Manchester The geometry of inverse semigroups, and uniform Roe algebras
Nathan Brownlowe , University of Sydney Self-similar quantum groups

Sponsors and Funders:

  • ICMS
  • GMJT
  • EMS