

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 [5,6,7,8,9], 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 [10,2,1,11,12]. 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.


NSF Research Training Grant at UC Berkeley on “Geometry, Topology and Operator Algebras”
Member, since 2008
Special semester on “4manifolds and their combinatorial invariants”
Max Planck Institute for Mathematics, Bonn, January  June, 2013,
joint with Michael Freedman and Matthias Kreck
Trimester program “Homotopy theory, manifolds and field theories”
Hausdorff Institute for Mathematics, Bonn, May  August, 2015,
joint with Soren Galatius, Haynes Miller and Stefan Schwede
Oberwolfach Workshops on “Topology” and “Topology and quantum field theory”
Organizer, 2010, 2012, 2014, 2016
Speaker on the International Max Planck Research School “Moduli Spaces”
DFG Cluster of Excellence “Hausdorff Center for Mathematics”
Principal Investigator


Research Area C With Stolz we developed functorial field theories for super symmetric Euclidean spacetimes. In [1] we show with Hohnhold and Kreck that the space of such dimensional Euclidean field theories is the classifying space for de Rham cohomology and in [2] we show that dimensional Euclidean field theories gives 8periodic Ktheory. This establishes a new relation between algebraic topology and quantum field theory and leads in particular to a precise mathematical understanding of deformations of functorial field theories.  Former Research Area F With Conant and Schneiderman, we show in [3] how to measure the failure of the Whitney move in dimension 4 by constructing higherorder intersection invariants of Whitney towers. We identify some of these new invariants with previously known link invariants like Milnor, SatoLevine and Arf invariants and define higherorder versions of the latter two types of invariants. These higherorder invariants are then shown to classify the existence of Whitney towers of increasing order in the 4ball.
Topological field theories are very successfull in dimensions 3 and 4. In fact, they are known to classify all closed 3manifolds, even with the (physically motivated) assumption of positivity. Moreover, all known 4manifold invariants can be formulated in terms of 4dimensional topological field theories. Freedman asked whether such statements continue to hold in higher dimensions and this was answered with Kreck in [4]: Simply connected 5manifolds are indeed classified by positive topological field theories but manifolds in higher dimensions are not. 


[ 1] 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[ 2] 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[ 4] Matthias Kreck, Peter Teichner
Positivity of topological field theories in dimension at least 5 J. Topol. , 1: (3): 663670 2008 DOI: 10.1112/jtopol/jtn016[ 5] Michael H. Freedman, Peter Teichner
4manifold topology. I. Subexponential groups Invent. Math. , 122: (3): 509529 1995 DOI: 10.1007/BF01231454[ 6] 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[ 7] 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[ 8] 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[ 9] J. Conant, R. Schneiderman, P. Teichner
Milnor invariants and twisted Whitney towers J. Topol. , 7: (1): 187224 2014 DOI: 10.1112/jtopol/jtt025[ 10] 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[ 11] 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[ 12] Stephan Stolz, Peter Teichner
Traces in monoidal categories Trans. Amer. Math. Soc. , 364: (8): 44254464 2012 DOI: 10.1090/S000299472012056157



• 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, University of Münster
Jim Conant (2000): “A Knot Bounding Grope of Class n is n/2 Trivial”,
now Professor, University of Tennessee, Knoxville, TN, USA
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 Advanced Researcher, Max Planck Institute for Mathematics, Bonn
Dmitri Pavlov (2011): “A decomposition theorem for noncommutative Lpspaces and a new symmetric monoidal bicategory of von Neumann algebras”,
now Postdoc, University of Regensburg


 PhD theses: 18, currently 5


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