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About me

I am a 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) in the topology group of Arthur Bartels 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

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