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*

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 [1,2,3,4,5], 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 [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.

Research Projects and Activities

Arbeitstagung on Physical Mathematics in honor of Yuri Manin,
Max Planck Institute for Mathematics in Bonn, June 19-23, 2017

“4-Manifolds and knot concordance”,
workshop organized at the Max-Planck Institute for Mathematics in Bonn, October 17-21, 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”

Contribution to Research Areas

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 Costello-Gwilliam 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 4-ball, 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 2-dimensional sheets and keeps pairing them with Whitney disks until a non-trivial 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 4-manifold the vanishing of the non-repeating part of the higher order intersection invariants is equivalent to the existence of immersions of 2-spheres in 4-manifolds with disjoint images.

Selected Publications

[1] Michael H. Freedman, Peter Teichner
4-manifold topology. I. Subexponential groups
Invent. Math. , 122: (3): 509--529
1995
[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 L2-signatures
Ann. of Math. (2) , 157: (2): 433--519
2003
[4] James Conant, Rob Schneiderman, Peter Teichner
Whitney tower concordance of classical links
Geom. Topol. , 16: (3): 1419--1479
2012
[5] J. Conant, R. Schneiderman, P. Teichner
Milnor invariants and twisted Whitney towers
J. Topol. , 7: (1): 187--224
2014
[6] 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
[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 : 207--274
Publisher: Amer. Math. Soc., Providence, RI
2010
[8] Henning Hohnhold, Matthias Kreck, Stephan Stolz, Peter Teichner
Differential forms and 0-dimensional supersymmetric field theories
Quantum Topol. , 2: (1): 1--41
2011
[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. : 279--340
Publisher: Amer. Math. Soc., Providence, RI
2011
[10] Stephan Stolz, Peter Teichner
Traces in monoidal categories
Trans. Amer. Math. Soc. , 364: (8): 4425--4464
2012
[11] Jim Conant, Rob Schneiderman, Peter Teichner
Cochran's β^i-invariants via twisted Whitney towers
J. Knot Theory Ramifications , 26: (2): 1740012, 28
2017
[12] Daniel Kasprowski, Markus Land, Mark Powell, Peter Teichner
Stable classification of 4-manifolds with 3-manifold fundamental groups
Journal of Topology , 10: (3): 827--881
2017
ISSN: 1753-8424
DOI: 10.1112/topo.12025

Publication List

MathSciNet Publication List (external link)

Editorships

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

Selected Invited Lectures

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

Offers

1999

University of Heidelberg

2004

Stanford University, CA, USA

2006

ETH Zürich, Switzerland

Selected PhD students

Arthur Bartels (1999): “Link Homotopy In Codimension Two”,
now Professor (W3), University of Münster

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 Assistant Professor, Notre Dame University, South Bend, Indiana, USA

Dmitri Pavlov (2011): “A decomposition theorem for noncommutative Lp-spaces 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 Berwick-Evans (2013): “Supersymmetric sigma models, partition functions and the Chern-Gauss-Bonnet Theorem”,
now Assistant Professor, University of Illinois at Urbana-Champaign, USA

Supervised Theses

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