Tobias Dyckerhoff

Research interests

higher category theory, noncommutative algebraic geometry, mathematical physics

Teaching

• Seminar: Noncommutative Hodge structures (Sommersemester 16, Bonn)
• Seminar: Fukaya categories and related topics (Wintersemester 15/16, Bonn)
• Advanced Algebra I: Homological Algebra (Sommersemester 15, Bonn)
• Advanced Topics in Algebra: Hall Algebras (Wintersemester 14/15, Bonn)
• Introduction to homological algebra (Hilary Term 2014, Oxford)
• Math 501: Modern Algebra II (Spring 2013, Yale)
• Math 425: Computational Algebraic Geometry (Spring 2012, Yale)
• Math 440: Introduction to Algebraic Geometry (Fall 2010, Yale)
• Math 371: Algebra (Summer 2009, Penn)
• Math 420: Ordinary Differential Equations (Summer 2008, Penn)
• Math 412: Linear Algebra (Summer 2007, Penn)

Publications/Preprints

• A1-homotopy invariants of topological Fukaya categories of surfaces
  Preprint: arXiv:1505.06941

• Higher categorical aspects of Hall algebras
  Preprint: arXiv:1505.06940

• Crossed simplicial groups and structured surfaces (joint with M. Kapranov)
  Preprint: arXiv:1403.5799 (to appear in Proceedings of CATS4)

• Higher Segal Spaces: Part II (joint with M. Kapranov)
  In preparation.

• Triangulated surfaces in triangulated categories (joint with M. Kapranov)
  Preprint: arXiv:1306.2545

• Higher Segal Spaces: Part I (joint with M. Kapranov)
  Preprint: arXiv:1212.3563 (accepted for publication in Springer Lecture Notes)

• Pushing forward matrix factorisations (joint with D. Murfet)
  Duke Math. J. Volume 162, Number 7 (2013), 1249-1311 (arXiv:1102.2957)

• The Kapustin-Li formula revisited (joint with D. Murfet)
  Advances in Mathematics 231 (2012), pp. 1858-1885 (arXiv:1004.0687)

• Compact generators in categories of matrix factorizations
  Duke Math. J. Volume 159, Number 2 (2011), 223-274 (arXiv:0904.4713)

• The inverse problem of differential Galois theory over the field R(z)
  Mathematisches Forschungsinstitut Oberwolfach Report No. 26/2007 (Preprint: arXiv:0802.2897)

• Picard-Vessiot extensions over number fields (Diplom thesis)

Selected invited talks

• ICM Satellite Conference on homological mirror symmetry and symplectic topology, POSTEC, Korea (August 2014)

• DFG Jahrestagung Darstellungstheorie, Soltau (March 2014)

• Matrix Factorizations in Algebra, Geometry and Physics, Oberwolfach Workshop (September 2013)

• AGNES Workshop, Yale (April 2013)

• MSRI Workshop on Representation Theory, Homological Algebra, and Free Resolutions, Berkeley (February 2013)

• Topology Seminar, Stanford University (January 2013)

• Conference on "Higher Categorical Structures and their Interactions with Algebraic Geometry, Algebraic Topology and Algebra", Luminy, France (July 2012)

• VIGRE Summer School on Algebraic Geometry, Working group leader on mirror symmetry, Athens, Georgia (May 2012)

• PASI conference on "Commutative Algebra and Its Interactions with Algebraic Geometry, Representation Theory, and Physics", Guanajuato, Mexico (May 2012)

• Indiana University, Bloomington (Nov 2011)

• Steklov Institute, Moscow, Conference on Derived Categories in Algebraic Geometry (Sep 2011)

• Universität Hannover (Jan 2011)

• Universität Wien (Jan 2011)

• Universität Bielefeld (Jan 2011)

• Universität Hamburg (Jan 2011)

• Ludwig-Maximilians-Universität München (Jan 2011)

• Osaka University, Mini Workshop on Mirror Symmetry of Singularities (Nov 2010)

• University of Miami, Workshop on Homological Mirror Symmetry and Related Topics (Jan 2010)

• University of Toronto, Homological Algebraic Geometry Seminar (Dec 2009)

• Columbia University, Algebraic Geometry Seminar (Nov 2009)

• University of Wisconsin-Madison, Algebraic Geometry Seminar (Nov 2009)

• GTEM Workshop on Constructive Galois Theory (Feb 2008)
  Title: Tutorial on differential Galois theory
  Slides:

  • Lecture 1
  • Lecture 2
  • Lecture 3

• MF Oberwolfach: Arithmetic and Differential Galois Groups (May 2007)
  Title: The inverse problem of differential Galois theory over the field R(z)
  Extended abstract: Oberwolfach Report No. 26/2007

• Kolchin Seminar in Differential Algebra (Dec 2005)
  Title: Picard-Vessiot theory over non-algebraically closed fields of constants