# SOAR members

Permanent staff

Ph.D. students and post-docs

Former students and post-docs

# Permanent staff

### Robert Archbold (University of Aberdeen)

Rob Archbold has recently moved to Emeritus status and maintains a wide interest in the area of operator algebras and the connections with groups and dynamical systems.

### Heiko Gimperlein (Heriot-Watt University)

Heiko obtained his Ph.D. at Leibniz Universität Hannover in 2010. After a postdoc in Copenhagen, he moved to Heriot-Watt in 2013. His research interests often center around harmonic analysis, with an emphasis on its applications. Connections to operator algebras sometimes happen through noncommutative geometry or the representation theory of Lie groups.

### Chris Heunen (University of Edinburgh)

Chris obtained his Ph.D. in 2009 from the Radboud University Nijmegen, the Netherlands, under supervision of Klaas Landsman and Bart Jacobs, on categorical models and logics for noncommutative operator algebras. After spending postdoc periods at Oxford and Caltech, he joined the University of Edinburgh in 2015, in the School of Informatics. He studies C*-algebras through their collection of commutative C*-subalgebras, as well as complete positivity and category theory, as semantic models for quantum computing.

### Mark V. Lawson (Heriot-Watt University)

Mark has worked at Heriot-Watt since 2004. In collaboration with Ganna Kudryavtseva (Ljubljana) and Daniel Lenz (Jena), he has been developing the theory of non-commutative Stone dualities. This originated in Renault's work connecting inverse semigroups, étale topological groupoids and C*-algebras and that of Kellendonk on aperiodic tilings. Recently, such dualities have led to connections with special subgroups of the group of homeomorphisms of the Cantor space as well as multiple-valued logic.

### Aaron Tikuisis (University of Aberdeen)

Aaron obtained his Ph.D. in 2011 from the University of Toronto, working on computations of the Cuntz semigroup under the supervision of George Elliott. After a post-doc in Münster, Aaron began in Aberdeen in 2013. He studies the classification and structure of C*-algebras, and is particularly interested in noncommutative covering dimension (nuclear dimension and decomposition rank) and their relationship to regularity properties such as Jiang-Su stability.

### Christian Voigt (University of Glasgow)

Christian obtained his Ph.D. at the University of Münster in 2003, studying equivariant cyclic homology under the direction of Joachim Cuntz. He then worked as a post-doc in Münster, Copenhagen and Göttingen before moving to Glasgow as a Lecturer in 2012. His research is focussed on the interplay between operator algebras and noncommutative geometry; more specifically Christian works on quantum groups and K-theory, and their connection with representation theory and the Baum-Connes conjecture.

### Simon Wassermann (University of Glasgow)

Simon Wassermann studies C*-algebras, especially tensor products and related notions. He is an Emiritus Reader at Glasgow.

### Stuart White (University of Glasgow)

Stuart completed his Ph.D. at the University of Edinburgh in 2006, studying structural properties of subalgebras of finite von Neumann factors with Allan Sinclair. He moved to Glasgow in 2007. Stuart has broad interests across operator algebras, studying both von Neumann algebras and C*-algebras, with a particular focus on the interplay and transfer of ideas between C*-algebras and von Neumann algebras. A key theme underpinning recent work is the development of coloured (i.e., higher dimensional) versions of von Neumann properties, in the topological setting of C*-algebras.

### Michael Whittaker (University of Glasgow)

Mike completed his Ph.D. entitled "Poincaré duality and spectral triples for hyperbolic dynamical systems" in 2010 at the University of Victoria, under the supervision of Ian Putnam. He spent 5 years as a post-doc in Wollongong before taking up a lectureship in Glasgow in 2015. Mike's primary research interest is the connection between topological dynamical systems and operator algebras. His specific interests in this area include C*-algebras associated with Smale spaces, self-similar group actions, graph and k-graph algebras, and aperiodic substitution tilings.

### John D. Maitland Wright (University of Aberdeen)

John has worked in Aberdeen since 2004. His wide interests among C*-algebras include an extensive study of monotone complete C*-algebras and their connections to generic dynamics.

### Joachim Zacharias (University of Glasgow)

Joachim obtained his Ph.D. at the University of Heidelberg, studying continuous analogues of Cuntz algebras under supervision of Joachim Cuntz. He then worked as a post-doc in Orleans and Paris 6 until taking up a lecturer position at the University of Nottingham in 2000. He moved subsequently to the University of Glasgow in 2012. His research is focussed on various example classes of C*-algebras (generalised Cuntz type algebras, crossed products and other classes), the interplay of operator algebras and dynamical systems, classification and dimension theories for C*-algebras and dynamical systems (e.g. nuclear dimension and Rokhlin dimension), topological approximation entropy, approximation properties with connections to coarse geometry.

# Ph.D. students and post-docs

### Joan Bosa (Beatriu de Pinós fellow, University of Glasgow)

Joan is a Catalan mathematician that completed his Ph.D. at Universitat Autonoma de Barcelona on September 2013, studying Continuous fields of C*-algebras and their Cuntz semigroups under the supervision of Francesc Perera. He then moved to University of Glasgow to work as part of the “The Cuntz Semigroup and the Fine Structure of Nuclear C*-Algebras” EPRSC project. His research lies in the interface between functional analysis, semigroups, groups and rings theory, and their relation to C*-algebras.

### Sam Evington (Ph.D. student, University of Glasgow)

Sam completed his M.Math. degree from Oxford University in 2013, then travelled north to begin his Ph.D. in Glasgow under the supervision of Stuart White. His research is inspired by the classification programme for simple, nuclear C*-algebras, and the various regularity properties for C*-algebras. He is currently on a quest to find a non-trivial tracially continuous W*-bundle.

### Ruardih Gardner (Ph.D. student, University of Aberdeen)

Ruaridh completed his M.Math. degree in the University of Edinburgh in 2016 and moved on to Aberdeen to begin his Ph.D. under the supervision of Aaron Tikuisis. He is interested in the classification of C*-algebras.

### Dimitrios Gerontogiannis (Ph.D. student, University of Glasgow)

Dimitrios obtained his B.Sc and M.Sc degree in mathematics at the National and Kapodistrian University of Athens. In 2016 he started his Ph.D. at the University of Glasgow under the supervision of Joachim Zacharias and Michael Whittaker. He is interested in the interplay between operator algebras and noncommutative geometry, specifically in noncommutative Poincaré duality formulated in the bivariant KK-theory of Kasparov.

### Luke Hamblin (Ph.D. student, University of Glasgow)

Luke completed his M.Math degree at the University of Warwick in 2015 before beginning his Ph.D. at the University of Glasgow under the supervision of Joachim Zacharias. His project concerns the Rokhlin dimension for actions on certain groups, with applications to the classification of C*-algebras.

### Andrew Monk (Ph.D. student, University of Glasgow)

Andrew completed his undergraduate degree at the University in Southampton in 2014 before moving to the University of Glasgow to start his Ph.D. under the supervision of Christian Voigt. His research project concerns the K-theory of complex quantum groups. Specifically the goal of the project is to try to obtain results analogous to the Baum-Connes conjecture for these quantum groups.

### Mustafa (Ismail) Ozkaraca (Ph.D. student, University of Glasgow)

Following his Masters degree in Bikent University, Ismail came to Glasgow to study for a Ph.D. funded by a scholarship from the Republic of Turkey's Ministry of National Education. He's working with Mike Whittaker on aperiodic substitution tilings and their C*-algebras.

### Gábor Szabó (Post-doc, University of Aberdeen)

Gábor obtained his Ph.D. at the University of Münster in 2015, studying Rokhlin dimension and topological dynamics under the supervision of Wilhelm Winter. He continued with a post-doc in Münster and began working in Aberdeen in 2016, as part of the EPSRC project “Regularity and dimension for C*-algebras”. His research focuses on the fine structure of simple C*-algebras and the classification of group actions on these object. He is also interested in the structure of crossed products, in particular regarding the interplay between C*-algebras and topological dynamics.