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About me

I am a Senior Lecturer in Algebra and Topology at Cardiff University and a member of the research group Geometry, Algebra, Mathematical Physics and Topology.

My research focuses on connections between operator algebras and algebraic topology, in particular (twisted) K-theory and index theory. I am also interested in topological and conformal field theories with a view towards elliptic cohomology.

Before joining the GAPT group at Cardiff University I was a post-doc (akademischer Rat auf Zeit) at the University of Münster. I received my PhD in Mathematics under supervision of Thomas Schick and my Diploma in Physics under supervision of Karl-Henning Rehren in Göttingen.

Recent Activities

With Ulrich Bunke and Markus Land I wrote a survey about KK-theory from a homotopical point of view. The preprint on the arXiv can be found here.
The next meeting of the research network Operator Algebras in the South of the UK will take place on Friday, 24th November 2023 in Bath. Details of the event can be found here.
Together with David Evans I finished the computation of the rational equivariant higher twisted K-groups of SU(n). The preprint can be found on the arXiv here.
I am co-organising a workshop with support from the Bremen-Cardiff collaboration fund. The title is Combinatorial Topology, Discrete Geometry and their Application to Data Science. It will take place on 12th September 2023 at Cardiff University. The details, registration page and schedule can be found here. Unfortunately, due to unforeseen circumstances this workshop had to be postponed.
It is my great pleasure to announce that the second meeting of the new network Operator Algebras in the South of the UK will take place on Friday, 19th May 2023 in Southampton.
I will give a talk at the British Topology Meeting 2023 in September 2023.
I will be at the Isaac Newton Institute in Cambridge from 26th June to 30th June 2023 for OAS Follow on: Operator Algebras: Subfactors and Applications.
I will be in Glasgow for a seminar talk from 22nd March to 24th March 2023
I will speak in the lunch-time seminar in Southampton on 20th March 2023
It is my great pleasure to announce that the first meeting of the new network Operator Algebras in the South of the UK will take place on Friday, 3rd March 2023 in Cardiff.
I am very glad that the conference "Operator Algebras: Subfactors, K-theory, Conformal Field Theory" that I am organising with Mathew Pugh and Gandalf Lechner will take place at Gregynog Hall from 27th July to 2nd August.
From 18th to 22nd July I am attending the LMS-INI-Bath Symposium on K-theory and Representation Theory.
From 30th May to 3rd June I will be at the Lorentz Centre for the conference "Non-commutative Geometry along the North Sea"
From 8th to 20th May 2022 I will be at the ICMS for a Research in Groups Meeting
A new preprint is now available on my Publications page: Equivariant Higher Dixmier-Douady Theory for Circle Actions on UHF-algebras . In this paper we start a programme to understand equivariant bundles of C*-algebras from a homotopy-theoretic viewpoint and in particular how these are linked to equivariant versions of the Brauer group.
I will speak in the Oberseminar Global Analysis and Geometry (Regensburg) on 9th February 2022.
On 7th January 2022 I gave a talk in the Oberseminar Topologie in Göttingen about equivariant higher twists over SU(n).
On 24th November 2021 I gave a seminar talk in Aberdeen about Exponential Functor Twists for K-theory over SU(n).
On 9th November 2021 gave a seminar talk in the Functional Analysis Seminar in Oxford about equivariant higher twists over SU(n).
From 20th September to 23rd September 2021 I attended the in-person workshop The unity of mathematics: A conference in honour of Sir Michael Atiyah at the Isaac Newton Institute.
From 21st June to 25th June 2021 I attended the online workshop Manifolds and K-theory: the legacy of Andrew Ranicki at the ICMS.
My PhD student Alvaro Torras Casas submitted his thesis. Congratulations!
On 11th May 2021 I gave a talk in the Operator Algebra in Oslo about equivariant higher twists over SU(n).
The preprint "Interleaving Mayer-Vietoris spectral sequences" that my PhD student Álvaro Torras wrote together with me is now available on the arXiv.
On 29th April 2021 I gave a talk in the "Regensburg Seminar in Homotopy Theory and Related Areas" about equivariant higher twists over SU(n).
On 28th January 2021 I gave a talk at the Institute for Pure and Applied Mathematics (IPAM) in the workshop Actions of Tensor Categories on C*-algebras with the title "Fell bundles, Dixmier-Douady theory and higher twists". A recording can be found here.
On 4th November 2020 I gave a talk in the Sheffield Pure Maths Colloquium on Google Meets with the title "Bundles of Algebras - Dixmier-Douady Theory and Beyond".
On 13th August I spoke in the UK Virtual Operator Algebras Seminar 2020 on Zoom about "Bundles of C*-Algebras - An introduction to Dixmier-Douady Theory". The slides can be found here.
I gave a talk in the Online Algebraic Topology Seminar (OATS) about K-theory in mathematical physics. A recording can be found here.
From 25th February to 13th March Taro Sogabe from Kyoto University will visit Cardiff.
I redesigned the problem sheets for MA2008 - Linear Algebra II this year. The lecture notes, problem sheets and solutions can be found here.
On 24th October I will give a talk in the Analysis Seminar in Glasgow.
On 11th October I will speak in the Pure Maths Colloquium in Southampton, where I will give a talk about "Loops, Groups and Twists".
On 3rd October I gave a talk in the seminar of the Algebraic Topology group in Sheffield, where I spoke about "Equivariant higher twisted K-theory of SU(n) via exponential functors".
I attended the 34th British Topology Meeting from 16th to 18th September in Warwick and gave a talk about equivariant higher twists over SU(n).
My PhD student Alvaro Torras Casas finished his first preprint titled "Distributing Persistent Homology via Spectral Sequences". It is available on the arXiv here.
The preprint "Equivariant higher twisted K-theory of SU(n) for exponential functor twists" is now available on the arXiv (see also this video). In this joint work with David E. Evans we compute the equivariant higher twisted K-groups of SU(n) for twistings induced by exponential functors. In all cases we analyse we always find a ring structure on these groups.
I was invited to visit the Simons Center from 9th June to 14th June 2019 for the programme "Operator Algebras and Quantum Physics".
I will attend the Topology Workshop that is part of the Intensive Research Programme LIGAT at the CRM in Barcelona from 17th June to 20th June.
On 8th March I attended the TTT109 in Leicester dedicated to the memory of Sir Michael Atiyah.
I am now the INI/ICMS-correspondent for the School of Mathematics at Cardiff University.
On 9th November 2018 I will speak in the Operator Algebra Seminar at KU Leuven about Connective C*-algebras.
On 16th to 17th November 2018 I will give a talk at the Barcelona Weekend on Operator Algebras at the CRM.
On 24th October I will give a talk about solutions to the Yang-Baxter equation and higher twists over SU(n) in the seminar of the algebra group at the University of Glasgow.
I attended the Dragon Applied Topology Conference in Swansea from 11th to 13th September 2018 together with my PhD student Alvaro Torras-Casas.
I visited Michael Joachim during the programme "Homotopy harnessing higher structures" at the Newton Institute in Cambridge. We continued our work on Adams operations on operator algebraic K-theory spectra.
I am now a Fellow of Advance HE (previously Higher Education Academy).
I will be at the Utrecht Topology Feest 2018 from 27th to 31st August.
Michael Joachim will visit Cardiff from 19th July to 25th July. We will continue our work on stable Adams operations via operator algebraic spectra of K-theory. He is funded by the Cardiff Incoming Visiting Fellowship Scheme.
I will attend the conference K-theory, Hecke Algebras and Representation Theory that takes place in Sheffield from 3rd to 6th July.
Together with my PhD student Alvaro Torras-Casas I attended a school on Topological Data Analysis and Persistent Homology in Levico Terme near Trento, Italy.
There is a new preprint on the Publications page titled "Exponential functors, R-matrices and Twists".
I will be visiting Copenhagen from 9th to 13th April and give a talk there as well.
Over the last semester I met with Padraig Corcoran, my PhD student Alvaro Torras Casas and Thomas Woolley for a fortnightly reading course on Topological Data Analysis
I will give a talk during the workshop of the LMS South Wales and South West Regional Meeting, 13th - 15th December 2017. I will speak about the joint work with Gandalf Lechner and Simon Wood (see below) on "Yang-Baxter representations of the infinite symmetric group". I will also give an introductory talk about topological quantum field theories on the same occasion.
The (german) lecture notes about TQFTs from a course I gave in Münster in the winter semester of 2011 can now be downloaded here.
From 16th - 26th January 2018 I will be visiting Prof. Masaki Izumi in Kyoto.
I will be visiting Glasgow on 10th October and give a talk in the Analysis Seminar about Connective C*-algebras.
Together with Gandalf Lechner and Simon Wood I published the preprint "Yang-Baxter representations of the infinite symmetric group". We classify all involutive solutions of the quantum Yang-Baxter equation on finite dimensional vector spaces.
I will attend the Research School on Algebraic Topology of Manifolds at the University of Oxford from 11th - 15th September 2017.
I successfully applied for funding from the "Cardiff Incoming Visiting Fellowship Scheme & International Collaboration Seedcorn Fund" to invite Michael Joachim from Münster to Cardiff in 2018. We will work on a project related to stable Adams operations on K-theory spectra using operator algebras. Together we will also visit Sheffield to work with John Greenlees, Paul Mitchener and Sarah Whitehouse.
During the Spring Semester 2017 I taught the course "MA3008 - Algebraic Topology" for the first time. Participants can find the lecture notes for the course on my publications page.
I will attend the workshop "Applications of operator algebras: order, disorder, symmetry" at the ICMS in Edinburgh from the 25th to the 30th June 2017.
I will attend the workshop "Subfactors, K-theory and conformal field theory" at the Newton Institute in Cambridge from the 13th to the 17th June 2017.
I visit Nils Waterstraat at the University of Kent from the 17th to the 19th of May and will also give a talk at a conference he organised. I will give an introduction to "Index theory, KK-theory and E-theory".
I will be at the workshop Subfactors, higher geometry, higher twists and almost Calabi-Yau algebras from 27th March to 31st March 2017 and give a talk about "Equivariant higher twisted K-theory".
From 5th April to the 29th April 2017 I will be attending the programme Operator algebras: subfactors and their applications at the Newton Institute.
On Thursday, the 24th of November 2016 I will be a speaker at the 101st meeting of the Transpennine Topology Triangle. The title of my talk is "Unit Spectra of K-theory via strongly self-absorbing C*-algebras".
On Wednesday, the 23rd of November I will visit the Department of Mathematical Sciences at the University of Loughborough and give a talk in the Analysis seminar about "Twisted index obstructions to positive scalar curvature"
On Friday, 2nd of December and Saturday, 3rd of December the workshop "Yang-Baxter equations: A Tangle of Physics and Mathematics" will take place here in Cardiff. Together with Gandalf Lechner and Simon Wood, I am one of the organisers.
From October 23rd to 29th 2016 I will attend a conference on Noncommutative index theory, which is part of the Simons Semester Noncommutative geometry the next generation at the Banach Center in Warsaw.
On October 13th I will give a talk about "Connective C*-algebras" in the Seminar of the Geometry, Algebra, Mathematical Physics and Topology Research Group.
On October 4th I will give a talk in the Algebra and Topology Seminar at Swansea University. The title of the talk is "Higher twisted K-theory via strongly self-absorbing C*-algebras".
From August 1st to 5th I will be at the 31st Summer Conference on Topology and its Applications in Leicester, where I will also give a talk on Friday. The title is "A non-commutative model for higher twisted K-theory".
On July 13th I finished my habilitation in Münster. My habilitation thesis about "Higher twisted K-theory" can be found on the publications page. I also gave a colloquium talk about the Erdös-Szekeres convex polygon problem (one of the requirements was that this talk should be unrelated to my research).
On May 24th I gave a talk about higher twists during the Wales Mathematics Colloquium in Gregynog Hall.
From April 14th to April 28th I visited Marius Dadarlat at Purdue University and gave a talk in the Wabash Modern Analysis Seminar
In April I started my new job as a lecturer at Cardiff University
From January 17th to February 06th 2016 I will be visiting the Institut Mittag-Leffler during the trimester Classification of Operator Algebras: Complexity, Rigidity and Dynamics
From October 1st to December 22nd 2015 I will be visiting Søren Eilers at the University of Copenhagen
During the summer semester 2015 I gave a lecture about K-Theory and the Hopf invariant
During the summer semester 2015 I organized a seminar about Cobordism Theory together with Michael Joachim
During the winter semester 2014/2015 I am organizing a seminar about Positive scalar curvature metricstogether with Johannes Ebert.
From October 6th to 9th I will be participating in the conference Methods of Noncommutative Geometry in Analysis and Topology in Hannover
During September I will participate in the trimester on Noncommutative Geometry and its Applications at the HIM in Bonn
From August 25th to August 29nd I will be visiting Glasgow for a masterclass on Classification, Structure, Amenability and Regularity
From August 18th to August 22nd I am organizing the meeting of the String Geometry Research Network in Münster
From July 20th to July 26th I will be visiting Marius Dadarlat at Purdue
From June 16th to June 20th I participated in the workshop C*-algebras and Dynamical Systems during the thematic program on Abstract Harmonic Analysis, Banach and Operator Algebras at the Fields Institute, where I gave a talk about topological invariants of C(X)-algebras