Profile
Profile

Prof. Dr. Tobias Dyckerhoff

Bonn Junior Fellow

E-mail: tobias.dyckerhoff(at)hcm.uni-bonn.de
Phone: +49 228 73 62225
Homepage: http://www.math.uni-bonn.de/people/dyckerho/
Room: 1.002
Location: Villa Maria
Institute: Mathematical Institute
Research Area: Research Area F*

Academic Career

2010

PhD in Mathematics, University of Pennsylvania, Philadelphia, PA, USA

2010 - 2013

Simons Postdoctoral Fellow, Yale University, New Haven, CT, USA

2013 - 2014

Titchmarsh Fellow, University of Oxford, England, UK

Since 2014

Bonn Junior Fellow, University of Bonn

Research Profile

My current work adresses various questions arising in derived noncommutative geometry described via differential graded categories. I am mainly interested in developing techniques which can be applied in the context of topological Fukaya categories. This is a circle of ideas inspired by a proposal of Kontsevich to provide a purely combinatorial description of Fukaya categories of Stein manifolds. With Kapranov, I have developed a systematic realization of a two-dimensional instance of this proposal using our theory of cyclic 2-Segal spaces. With Brav, I am working on relative variants of various notions of a noncommutative Calabi-Yau structures which are amenable to gluing procedures for topological Fukaya categories of surfaces. In work in progress, we are analyzing the relation to shifted symplectic geometry. In another work, I have calculated A^1-homotopy invariants of two-dimensional topological Fukaya categories.

My future research plans include a systematic realization of Kontsevich's proposal in higher dimensions based on the theory of structured higher Segal spaces. With Kapranov, Schechtman, and Soibelman, we have are working on a theory of topological Fukaya categories with coefficients for surfaces. In future work, we hope to apply this theory to provide new descriptions of various interesting categories arising in representation theory and mirror symmetry. With Brown and Blanc, we are developing an approach to topological KR-theory for real differential graded categories. One of our main goals are interesting applications in noncommutative singularity theory. Further, I hope to investigate the relevance of the theory of higher Segal spaces in the context of Hall algebras.

Selected Publications

[1] T. Dyckerhoff, M. Kapranov
Crossed simplicial groups and structured surfaces
Stacks and categories in geometry, topology, and algebra
of Contemp. Math. : 37--110
Publisher: Amer. Math. Soc., Providence, RI
2015
[2] Tobias Dyckerhoff, Daniel Murfet
Pushing forward matrix factorizations
Duke Math. J. , 162: (7): 1249--1311
2013
[3] Tobias Dyckerhoff, Daniel Murfet
The Kapustin-Li formula revisited
Adv. Math. , 231: (3-4): 1858--1885
2012
[4] Tobias Dyckerhoff
Compact generators in categories of matrix factorizations
Duke Math. J. , 159: (2): 223--274
2011
[5] Tobias Dyckerhoff
Isolated hypersurface singularities as noncommutative spaces
Thesis (Ph.D.)--University of Pennsylvania
Publisher: ProQuest LLC, Ann Arbor, MI
2010
ISBN: 978-1124-32510-1

Publication List

Editorships

• Higher Structures (since 2016)

Selected Invited Lectures

2011

Steklov Institute, Moscow, Russia

2012

PASI, Guanajuato, Mexico

2013

Topology Seminar, Stanford University, CA, USA

2013

AGNES Workshop, Yale, CT, USA

2014

ICM Satellite Conference on Homological mirror symmetry and symplectic topology, POSTEC, Korea

2015

Kolloquium, Münster

2015

Kolloquium, Hamburg

Supervised Theses

  • Master theses: 2, currently 2
  • PhD theses: 2, currently 2
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