Profile
Profile

Prof. Dr. Peter Teichner

E-mail: teichner(at)mpim-bonn.mpg.de
Phone: +49 228 402 202
Homepage: http://www.mpim-bonn.mpg.de/node/98
Location: Max-Planck-Institute for Mathematics
Institute: Max-Planck-Institute for Mathematics
Research Areas: Research Area C
Research Area F*
Former Research Area E
Birthdate: 30.Jun 1963
Mathscinet-Number: 335816

Academic Career

1990 - 1992

Scientific Assistant, University of Mainz

1992

PhD, University of Mainz

1992 - 1995

Feodor-Lynen 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

Research Profile

I study the impact of physics on topology. One focus is on classification results for knots, links and 4-dimensional manifolds [5,6,7,8,9], particularly by developing the theory of Whitney towers in 4-manifolds 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.

Research Projects and Activities

NSF research training grant at UC Berkeley on “Geometry, Topology and Operator Algebras”
Member, since 2008

4-Manifolds and their combinatorial invariants
Special semester at the Max-Planck Institute for Mathematics in Bonn, January - June, 2013,
joint with Michael Freedman and Matthias Kreck

Homotopy theory, manifolds and field theories
Trimester program at the Hausdorff Institute for Mathematics in 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

Contribution to Research Areas

Research Area C
With Stolz we developed functorial field theories for super symmetric Euclidean space-times. In [1] we show with Hohnhold and Kreck that the space of such 0|1-dimensional Euclidean field theories is the classifying space for de Rham cohomology and in [2] we show that 1|1-dimensional Euclidean field theories gives 8-periodic K-theory. 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 higher-order intersection invariants of Whitney towers. We identify some of these new invariants with previously known link invariants like Milnor, Sato-Levine and Arf invariants and define higher-order versions of the latter two types of invariants. These higher-order invariants are then shown to classify the existence of Whitney towers of increasing order in the 4-ball.
Topological field theories are very successfull in dimensions 3 and 4. In fact, they are known to classify all closed 3-manifolds, even with the (physically motivated) assumption of positivity. Moreover, all known 4-manifold invariants can be formulated in terms of 4-dimensional topological field theories. Freedman asked whether such statements continue to hold in higher dimensions and this was answered with Kreck in [4]: Simply connected 5-manifolds are indeed classified by positive topological field theories but manifolds in higher dimensions are not.
Research Area F*

Selected Publications

[1] Henning Hohnhold, Matthias Kreck, Stephan Stolz, Peter Teichner
Differential forms and 0-dimensional supersymmetric field theories
Quantum Topol. , 2: (1): 1--41
2011
ISSN: 1663-487X
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 : 207--274
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): 663--670
2008
ISSN: 1753-8416
DOI: 10.1112/jtopol/jtn016
[5] Michael H. Freedman, Peter Teichner
4-manifold topology. I. Subexponential groups
Invent. Math. , 122: (3): 509--529
1995
ISSN: 0020-9910
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 L2-signatures
Ann. of Math. (2) , 157: (2): 433--519
2003
ISSN: 0003-486X
DOI: 10.4007/annals.2003.157.433
[8] James Conant, Rob Schneiderman, Peter Teichner
Whitney tower concordance of classical links
Geom. Topol. , 16: (3): 1419--1479
2012
ISSN: 1465-3060
DOI: 10.2140/gt.2012.16.1419
[9] J. Conant, R. Schneiderman, P. Teichner
Milnor invariants and twisted Whitney towers
J. Topol. , 7: (1): 187--224
2014
ISSN: 1753-8416
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. : 247--343
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. : 279--340
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): 4425--4464
2012
ISSN: 0002-9947
DOI: 10.1090/S0002-9947-2012-05615-7

Publication List

Editorships

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

Selected Invited Lectures

2002

Invited speaker, ICM, Beijing, China

2008

Plenary speaker, Annual Meeting of the A.M.S., San Diego, CA, USA

2008

Three “Simons Lectures” at Massachusetts Institute of Technology, MA, USA

2012

Three ''Andrzej Jankowski Memorial Lectures” at Unversity of Gdansk, Poland

2012

Two “Ritt Lectures” at Columbia University, NYC, USA

Offers

1999

University of Heidelberg

2004

University of Stanford, CA, USA

2006

ETH Zürich, Switzerland

Selected PhD students

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 Bismut-Chern Character”,
now Associate Professor, National University of Singapore

Chris Schommer-Pries (2009): “The Classification of Two-Dimensional Extended Topological Field Theories”,
now Advanced Researcher, Max Planck Institute for Mathematics, Bonn

Dmitri Pavlov (2011): “A decomposition theorem for noncommutative Lp-spaces and a new symmetric monoidal bicategory of von Neumann algebras”,
now Postdoc, University of Regensburg

Supervised Theses

  • PhD theses: 18, currently 5
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