

1990  1992  Scientific Assistant, University of Mainz  1992  PhD, University of Mainz  1992  1995  FeodorLynen Fellowship (Humboldt Stiftung), University of California, San Diego, CA, USA  1995  1996  Scientific Assistant, University of Mainz  1996  1997  Miller Research Fellow, University of California, Berkeley, CA, USA  1996  1999  Associate Professor, University of California, San Diego, CA, USA  1999  2004  Professor, University of California, San Diego, CA, USA  Since 2004  Professor, University of California, Berkeley, CA, USA  Since 2008  Scientific Member and Director, Max Planck Institute for Mathematics, Bonn 


I study the impact of physics on topology. One focus is on classification results for knots, links and 4dimensional manifolds [1,2,3,4,5], particularly by developing the theory of Whitney towers in 4manifolds with Jim Conant and Rob Schneiderman. We hope that they will become essential tools for the main open problems in dimension 4, the topological surgery sequence for arbitrary fundamental groups as well as the smooth Schoenfliess conjecture.
Another focus is on developing a mathematical notion of super symmetric quantum field theories, joint with Stephan Stolz and many others [6,7,8,9,10]. We are relating the spaces of specific types of geometric field theories to the classifying spaces of certain generalized cohomology theories. The hope is that successful tools of algebraic topology will be able to predict interesting results about the deformation classes of quantum field theories. Currently, we are connecting the world of factorization algebras to our notion of field theories, allowing us to express many physically relevant field theories our language.


Arbeitstagung on Physical Mathematics in honor of Yuri Manin,
Max Planck Institute for Mathematics in Bonn, June 1923, 2017
“4Manifolds and knot concordance”,
workshop organized at the MaxPlanck Institute for Mathematics in Bonn, October 1721, 2016
Trimester program “Homotopy theory, manifolds and field theories”,
Hausdorff Institute for Mathematics, Bonn, May  August, 2015,
organized jointly with Soren Galatius, Haynes Miller and Stefan Schwede
Oberwolfach Workshops on “Topology” and “Topology and quantum field theory”
Organizer, 2010, 2012, 2014, 2016, 2018
Speaker of the International Max Planck Research School on “Moduli Spaces”


Research Area C Stolz, Teichner and many others developed a mathematical approach to super symmetric field theories, in terms of functors on geometric bordism categories. The focus is on connections to algebraic topology, in particular elliptic cohomology and the relation to the CostelloGwilliam approach to observables in QFT via factorization algebras. A recent result constructs a twisted functorial field theory out of a factorization algebra, importing perturbative methods into the functorial point of view.  Research Area F* Conant, Schneiderman and Teichner developed the theory of Whitney towers. In the 4ball, they are understood by higher order intersection invariants with values in a certain group generated by trivalent trees. Roughly speaking, one looks at intersections of 2dimensional sheets and keeps pairing them with Whitney disks until a nontrivial count arises.
This basic work has been applied to various problems of low dimensional manifold theory, for example to classification of string links and geometric understanding of Cochran’s invariants. Schneiderman and Teichner showed that in an arbitrary 4manifold the vanishing of the nonrepeating part of the higher order intersection invariants is equivalent to the existence of immersions of 2spheres in 4manifolds with disjoint images. 


[ 1] Michael H. Freedman, Peter Teichner
4manifold topology. I. Subexponential groups Invent. Math. , 122: (3): 509529 1995 DOI: 10.1007/BF01231454[ 2] Peter Teichner
Knots, von Neumann signatures, and grope cobordism Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002) Publisher: Higher Ed. Press, Beijing 2002[ 3] Tim D. Cochran, Kent E. Orr, Peter Teichner
Knot concordance, Whitney towers and L^{2}signatures Ann. of Math. (2) , 157: (2): 433519 2003 DOI: 10.4007/annals.2003.157.433[ 4] James Conant, Rob Schneiderman, Peter Teichner
Whitney tower concordance of classical links Geom. Topol. , 16: (3): 14191479 2012 DOI: 10.2140/gt.2012.16.1419[ 5] J. Conant, R. Schneiderman, P. Teichner
Milnor invariants and twisted Whitney towers J. Topol. , 7: (1): 187224 2014 DOI: 10.1112/jtopol/jtt025[ 6] Stephan Stolz, Peter Teichner
What is an elliptic object? Topology, geometry and quantum field theory of London Math. Soc. Lecture Note Ser. : 247343 Publisher: Cambridge Univ. Press, Cambridge 2004 DOI: 10.1017/CBO9780511526398.013[ 7] Henning Hohnhold, Stephan Stolz, Peter Teichner
From minimal geodesics to supersymmetric field theories A celebration of the mathematical legacy of Raoul Bott of CRM Proc. Lecture Notes : 207274 Publisher: Amer. Math. Soc., Providence, RI 2010[ 8] Henning Hohnhold, Matthias Kreck, Stephan Stolz, Peter Teichner
Differential forms and 0dimensional supersymmetric field theories Quantum Topol. , 2: (1): 141 2011 DOI: 10.4171/QT/12[ 9] Stephan Stolz, Peter Teichner
Supersymmetric field theories and generalized cohomology Mathematical foundations of quantum field theory and perturbative string theory of Proc. Sympos. Pure Math. : 279340 Publisher: Amer. Math. Soc., Providence, RI 2011 DOI: 10.1090/pspum/083/2742432[ 10] Stephan Stolz, Peter Teichner
Traces in monoidal categories Trans. Amer. Math. Soc. , 364: (8): 44254464 2012 DOI: 10.1090/S000299472012056157[ 11] Jim Conant, Rob Schneiderman, Peter Teichner
Cochran's β^iinvariants via twisted Whitney towers J. Knot Theory Ramifications , 26: (2): 1740012, 28 2017 DOI: 10.1142/S0218216517400120[ 12] Daniel Kasprowski, Markus Land, Mark Powell, Peter Teichner
Stable classification of 4manifolds with 3manifold fundamental groups Journal of Topology , 10: (3): 827881 2017 ISSN: 17538424 DOI: 10.1112/topo.12025




• Geometry & Topology (since 2004)
• Forum of Mathematics, Sigma and Pi (since 2012), Open Access Journals


2002  Invited speaker, International Congress of Mathematicians, Beijing, China  2008  Plenary speaker, Annual Meeting of the AMS, San Diego, CA, USA  2008  Three “Simons Lectures”, Massachusetts Institute of Technology, MA, USA  2012  Three “Andrzej Jankowski Memorial Lectures”, Unversity of Gdansk, Poland  2012  Two “Ritt Lectures”, Columbia University, NYC, USA 


1999  University of Heidelberg  2004  Stanford University, CA, USA  2006  ETH Zürich, Switzerland 


Arthur Bartels (1999): “Link Homotopy In Codimension Two”,
now Professor (W3), University of Münster
Fei Han (2008): “Supersymmetric QFTs, Super Loop Spaces and BismutChern Character”,
now Associate Professor, National University of Singapore
Chris SchommerPries (2009): “The Classification of TwoDimensional Extended Topological Field Theories”,
now Assistant Professor, Notre Dame University, South Bend, Indiana, USA
Dmitri Pavlov (2011): “A decomposition theorem for noncommutative Lpspaces and a new symmetric monoidal bicategory of von Neumann algebras”,
now Assistant Professor, Texas Tech University, USA
Qin Li (2011): “Pontrjagin forms on certain string homogeneous spaces”,
now Assistant Professor, Southern University of Science and Technology, Shenzhen, China
Dan BerwickEvans (2013): “Supersymmetric sigma models, partition functions and the ChernGaussBonnet Theorem”,
now Assistant Professor, University of Illinois at UrbanaChampaign, USA


 Master theses: 7, currently 1
 PhD theses: 18, currently 7


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