Dr Ulrich Pennig

(he/him)

Publication

• Date
• Type

Research

My research interests in a nutshell

My main research interest is algebraic topology. A topology on a space allows us to talk about closeness or neighbourhoods of points without actually having to talk about distances between them. This enables us to define continuity of maps as well. Many geometric objects, like surfaces or higher dimensional manifolds, are in particular topological spaces. The goal of algebraic topology is to associate algebraic invariants, often groups, rings or modules, to these spaces in a natural way to distinguish them up to homotopy equivalence, i.e. up to continuous deformations.

An important example of such an invariant is topological K-theory. It is a generalised cohomology theory, which means that it satisfies axioms that allow its computation from a decomposition of the space into smaller parts. It can be defined as an invariant associated to the algebra of continuous functions on the space (vanishing at infinity) and as such it can be generalised to noncommutative algebras, which should be considered as "noncommutative topological spaces". These operator algebras not only play an important role in mathematical physics, they also can be used to describe highly singular topological spaces, like orbifolds or foliations.

K-theory has many different variants, like equivariant K-theory or twisted K-theory. The outcome of one of my research projects, which was joint work with Marius Dadarlat, was a description of twisted K-theory via operator algebras that includes the higher twists, a feature of the theory, which was formerly only accessible via homotopy theory.

I am interested in these and other interactions between algebraic topology, homotopy theory and operator algebras. Since I studied mathematical physics before my PhD, I am also interested in topological and conformal field theories and their connection with another generalised cohomology theory, called elliptic cohomology.

Recent Conference Organisation

09/09/2025 - 11/09/2025: 38th British Topology Meeting
07/03/2025 - 07/03/2025: Operator Algebras in the South of the UK
(with Veronique Fischer, Jan Spakula and Stuart White)
06/09/2024 - 07/09/2024: Operator Algebras in the South of the UK
15/03/2024 - 16/03/2024: Operator Algebras in the South of the UK
24/11/2023 - 24/11/2023: Operator Algebras in the South of the UK
19/05/2023 - 19/05/2023: Operator Algebras in the South of the UK
19/05/2023 - 19/05/2023: Operator Algebras in the South of the UK
03/03/2023 - 03/03/2023: Operator Algebras in the South of the UK
27/07/2022 - 02/08/2022: Operator Algebras: Subfactors, K-Theory, Conformal Field Theory
(with Masaki Izumi, Gandalf Lechner, Mathew Pugh)
08/05/2022 - 20/05/2022: Research in Groups at the ICMS
(with Christian Voigt)

Selected Conference and Seminar Talks

01/2025: Interactions between C*-algebraic KK-theory and homotopy theory, online 
12/2024: 121st Meeting of the Transalpine Topology Tetrahedron, Sheffield
12/2024: New trends at the intersection of quantum information theory, quantum groups and operator algebras, Isaac Newton Institute, Cambridge 
10/2024: SFB-Seminar, Regensburg
06/2024: GeNoCAS 2024
06/2024: UK Operator Algebras Conference
11/2023: Twinned Conference on C*-Algebras and Tensor Categories
09/2023: British Topology Meeting 
03/2023: Lunch time seminar, Southampton
03/2023: Analysis Seminar, Glasgow
06/2022: Non-commutative Geometry along the North Sea (Lorentz Center, Leiden)
Bundles of C*-Algebras and Higher Dixmier-Douady Theory
02/2022: Oberseminar Global Analysis and Geometry (Regensburg) 
Equivariant Higher Dixmier-Douady Theory for Circle Actions
01/2022: Oberseminar Topologie Göttingen
Equivariant higher twists over SU(n)
11/2021 University of Aberdeen 
Exponential Functor Twists for K-theory over SU(n)
11/2021 Functional Analysis Seminar, Oxford 
Equivariant higher twists over SU(n)
04/2021: Operator Algebra Seminar Oslo
Equivariant higher twists over SU(n)
04/2021: Regensburg Seminar in Homotopy Theory and Related Areas
Equivariant higher twists over SU(n)
01/2021: Institute for Pure & Applied Mathematics (IPAM)
Fell bundles, Dixmier-Douady theory and higher twists (video)
11/2020: Sheffield Pure Maths Colloquium
Bundles of Algebras - Dixmier-Douady Theory and Beyond
08/2020: UK Virtual Operator Algebra Seminar
Bundles of C*-Algebras - An introduction to Dixmier-Douady Theory
05/2020: Online Algebraic Topology Seminar (OATS)
Loops, Group and Twists - The role of K-theory in mathematical physics (video)
10/2019: Pure Maths Colloquium, Southampton
Loops, Groups and Twists - the role of K-theory in mathematical physics
10/2019: Topology Seminar, Sheffield
Equivariant higher twisted K-theory of SU(n) via exponential functors
10/2019: Operator Algebra Seminar, Glasgow
Equivariant higher twisted K-theory of SU(n) via exponential functors
09/2019: 34th British Topology Meeting, Warwick
Equivariant higher twisted K-theory of SU(n) via exponential functors
06/2019: Operator Algebras and Quantum Physics, Simons Center New York
Equivariant higher twisted K-theory of SU(n) via exponential functors
11/2018: Barcelona Weekend on Operator Algebras
Connective C*-algebras
10/2018: Algebra Seminar, Glasgow
The Yang-Baxter equation and higher twists over SU(n)
11/2018: Operator Algebra Seminar, KU Leuven
Connective C*-algebras
04/2018: Operator Algebra Seminar, Copenhagen
Connective C*-algebras
01/2018: Kyoto Operator Algebra Seminar
A Dixmier-Douady Theory for strongly self-absorbing C*-algebras
10/2017: Analysis Seminar, Glasgow
Connective C*-algebras
03/2017: Newton Institute, Cambridge
Equivariant Higher Twisted K-theory
11/2016: 101st Meeting of the Transpennine Topology Triangle, Leicester
Unit Spectra of K-theory via strongly self-absorbing C*-algebras
11/2016: Analysis Seminar, Loughborough
Twisted index obstructions to positive scalar curvature
10/2016: Algebra and Topology Seminar, Swansea
Higher twisted K-theory via strongly self-absorbing C*-algebras
08/2016: 31st Summer Conference on Topology and its Applications, Leicester
A non-commutative model for higher twisted K-theory
04/2016: Wabash Analysis Seminar
Deformations of nilpotent groups and homotopy symmetric C*-algebras
03/2016: Analysis Seminar, Glasgow
Deformations of nilpotent groups and homotopy symmetric C*-algebras
03/2016: Topology Seminar, Aberdeen
Higher twisted K-theory via strongly self-absorbing C*-algebras
10/2015: Operator Algebra Seminar, Copenhagen
Deformations of nilpotent groups and homotopy symmetric C*-algebras
06/2015: Oberwolfach Workshop “Noncommutative Geometry”
A Dixmier-Douady Theory for strongly self-absorbing C*-algebras
03/2015: Operator Algebra Seminar, Copenhagen (invited by Dominic Enders)
A noncommutative model for higher twisted K-theory and K-homology
02/2015: String Geometry Network Meeting, Greifswald
Crossed module actions on continuous trace C*-algebras
11/2014: Geometry and Quantum Theory, Zandvoort (invited by Maarten Solleveld)
Twisted index obstructions to positive scalar curvature
10/2014: Methods of Noncommutative Geometry in Analysis and Topology, Hannover
A Dixmier-Douady Theory for strongly self-absorbing C*-algebras
09/2014: Quantum physics and non-commutative geometry
during the trimester: Non-commutative Geometry and its Applications, HIM Bonn
Twisted K-theory via strongly self-absorbing C*-algebras
07/2014: C*-Algebras and Dynamical Systems, Fields Institute, Toronto
Topological invariants of C(X)-algebras
11/2013: Analysis Seminar, Glasgow (invited by Christian Voigt)
Unit spectra of K-theory via strongly self-absorbing C*-algebras
10/2013: Twists, generalised cohomology and applications, Münster
Unit spectra of K-theory via strongly self-absorbing C*-algebras
10/2013: String Geometry Network Meeting, MPI, Bonn
Unit spectra of K-theory via strongly self-absorbing C*-algebras
09/2013: Séminaires de l'équipe de Topologie Algébrique, Paris (invited by Christian Ausoni)
Unit spectra of K-theory via strongly self-absorbing C*-algebras
09/2013: Operator Algebras Seminar at Purdue (invited by Marius Dadarlat)
Unit spectra of K-theory via strongly self-absorbing C*-algebras
09/2013: Berkeley Topology Seminar (invited by Constantin Teleman)
K-theory, BU and C*-algebras (Introductory Talk)
Unit spectra of K-theory via strongly self-absorbing C*-algebras (Main Talk)
04/2013: Operator Algebras Seminar at Purdue (invited by Marius Dadarlat)
Operator algebraic K-theory via spectra
04/2013: ICMS-Workshop: The structure and classification of nuclear C*-algebras, Edinburgh
A Dixmier-Douady Theory for strongly self-absorbing C*-algebras
08/2012: Strings and Automorphic Forms in Topology, Bochum
Higher Twisted K-theory
06/2012: Young Topologists Meeting 2012, Copenhagen
Higher Twisted K-theory
05/2012: 17th NRW Topology, Münster
Twisted 2-vector bundles

Research visits

04/11/2024 - 06/12/2024: Isaac Newton Instiute, Cambridge
14/10/2024 - 23/10/2024: Universität Regensburg
29/09/2024 - 13/10/2024: Georg-August-Universität Göttingen
17/05/2024 - 23/05/2024: Dublin Institute of Advanced Studies (DIAS)
26/06/2023 - 30/06/2023: Isaac Newton Institute, Cambridge
20/09/2021 - 23/09/2021: Isaac Newton Instiute, Cambridge
09/06/2019 - 14/06/2019: Simons Center for Geometry and Physics, New York
09/04/2018 - 13/04/2018: University of Copenhagen, Denmark
16/01/2018 - 26/01/2018: Kyoto University, Japan
14/06/2017 - 17/06/2017: Isaac Newton Institute, Cambridge
05/04/2017 - 29/04/2017: Isaac Newton Institute, Cambridge
26/03/2017 - 31/03/2017: Isaac Newton Institute, Cambridge
14/04/2016 – 28/04/2016: Purdue University, West Lafayette
18/01/2016 – 07/02/2016: Institut Mittag-Leffler, Djursholm
01/10/2015 – 22/12/2015: Centre for Symmetry and Deformation, Copenhagen
23/02/2015 – 27/02/2015: String Geometry Network Meeting, Greifswald
01/09/2014 – 30/09/2014: HIM, Bonn (trimester on non-commutative geometry)
20/07/2014 – 26/07/2014: Purdue University, West Lafayette
24/02/2014 – 28/02/2014: String Geometry Network Meeting, ESI, Vienna
07/10/2013 – 11/10/2013: String Geometry Network Meeting, MPI, Bonn
30/09/2013 – 04/10/2013: Charles University, Prague
14/09/2013 – 20/09/2013: Purdue University, West Lafayette
08/09/2013 – 13/09/2013: University of California, Berkeley
28/04/2013 – 09/05/2013: Purdue University, West Lafayette
18/02/2013 – 22/02/2013: String Geometry Network Meeting, Regensburg
03/12/2012 – 08/12/2012: Charles University, Prague
22/05/2012 – 26/05/2012: String Geometry Network Meeting, Hamburg
20/04/2012 – 27/04/2012: Purdue University, West Lafayette

Teaching

Teaching

MA3008 - Algebraic Topology (Spring 2025)
MA3008 - Algebraic Topology (Spring 2024)
MA1005 - Foundations of Mathematics I (Autumn 2023) 
MA3008 - Algebraic Topology (Spring 2023)
MA1005 - Foundations of Mathematics I (Autumn 2022)
MA3008 - Algebraic Topology (Spring 2022)
MA1005 - Foundations of Mathematics I (Autumn 2021)
MA3008 - Algebraic Topology (Spring 2021)
MA1005 - Foundations of Mathematics I (Autumn 2020)
MA3008 - Algebraic Topology (Spring 2020)
MA2008 - Linear Algebra II (Autumn 2019)
MA3008 - Algebraic Topology (Spring 2019)
MA2008 - Linear Algebra II (Autumn 2018)
MA3008 - Algebraic Topology (Spring 2018)
MA2007 - Linear Algebra (Autumn 2017)
MA3008 - Algebraic Topology (Spring 2017)

Previous Teaching

K-theory and the Hopf invariant (summer semester 2015, University of Münster)
Topological Quantum Field Theories (winter semester 2011/12, University of Münster)

Biography

Qualifications

07/2016 – Habilitation (University of Münster)
08/2009 – Doctor rer. nat. in Mathematics (University of Göttingen)
05/2006 – Diploma in Theoretical Physics (University of Göttingen)

Honours and awards

05/2017: Nomination for the Philip Leverhulme Prize
10/2010: Dissertation Prize 2009 of the Universitätsbund Göttingen
08/2006 – 06/2009: PhD Scholarship of the German National Academic Foundation
04/2003 – 05/2006: Diploma Scholarship of the German National Academic Foundation

Academic positions

11/2010 – 04/2016: Akademischer Rat auf Zeit (University of Münster)
08/2010 – 10/2010: Research Assistant (University of Münster)
12/2009 – 07/2010: Akademischer Rat auf Zeit (University of Göttingen)
09/2009 – 11/2009: Research Assistant (Courant Research Center, Göttingen)

Committees and reviewing

Reviewer for

• Inventiones Mathematicae
• Advances in Mathematics
• Journal of Functional Analysis
• Algebraic & Geometric Topology
• Mathematical Physics, Analysis and Geometry
• Transactions of the AMS
• International Mathematics Research Notices
• Reviews in Mathematical Physics

Supervisions

Research Areas for Potential PhD projects:

• algebraic topology, operator-algebraic and topological K-theory and its variants (twisted, equivariant, ...)
• operator algebras, applications of homotopy theory to the theory of C*-algebras
• index theory

Current supervision

Valerio Bianchi

Declan Bays

George Tridimas

Past projects

• Sam Richardson (viva in 2022) worked on the computation of rational characteristic classes associated to maps induced by exponential functors on vector spaces (thesis)
• Álvaro Torras Casas (viva in 2022) worked on distributed computation of persistent homology using the Mayer-Vietoris spectral sequence (paper in Discrete & Computational Geometry, arxiv link)