Dr Ulrich Pennig

Dr Ulrich Pennig

Lecturer

School of Mathematics

Research Group

Geometry, Algebra, Mathematical Physics and Topology

Research Interests

My research interests are connections between algebraic topology, homotopy theory and operator algebras, in particular (twisted) K-theory and index theory. Since I studied theoretical physics before my PhD, I am also interested in topological and conformal field theories with a view towards elliptic cohomology.

Personal Webpage

http://upennig.weebly.com

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

  • 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

2018

2017

2016

2015

2014

2011

2007

Teaching 

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)

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.

Conferences organised

02/12/2016 - 03/12/2016: Yang-Baxter Equations: A Tangle of Physics and Mathematics
(with Gandalf Lechner and Simon Wood)
18/08/2014 – 22/08/2014: String Geometry Network Meeting, Münster
11/09/2012 – 14/09/2012: From Poisson to String Geometry, Erlangen
(with Catherine Meusburger, Thomas Nikolaus,
Christoph Schweigert and Christoph Wockel)
28/08/2006 – 02/09/2006: Young topologists and new topology, Bedlewo
(with Thomas Schick and Stanislav Spiez)

Selected Conference and Seminar Talks

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)
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

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

Current supervision

Alvaro Torras Casas profile picture

Alvaro Torras Casas

Research student