Tobias Dyckerhoff

Address	Universität Hamburg Fachbereich Mathematik Bundesstraße 55 20146 Hamburg
Room	Geomatikum 338
Office Hours	By appointment (click here to enter BBB office hour)
Phone	+49 40 42838-5152
Email	tobias.dyckerhoff AT uni-hamburg.de
Public Key	public.pgp
	@tobias.dyckerhoff:matrix.math.uni-hamburg.de
	tube.octaplex.net

I am a professor at the University of Hamburg affiliated with:

• Bereich Algebra und Zahlentheorie
• Collaborative research center 1624: Higher structures, moduli spaces, and integrability
• Center for mathematical physics Hamburg
• Quantum Universe

Visit our joint event calendar containing events of interest to the groups "Analysis and Differential Geometry (AD)" and "Algebra and Number Theory (AZ)".

Events

Workshop on higher categorical methods in algebra and geometry, March 22 - 24, 2023 (Hamburg).

• https://www.math.uni-hamburg.de/home/dyckerhoff/hcm23/

Research interests

higher structures in algebra and geometry

Research group

Current members	Angus Rush Till Heine Matthew Habermann Jonte Gödicke Laura Kähler Niklas Spangenberg Simon Schneider
Former members	Merlin Christ Fernando Abellán Garcia Xinyang Liu Walker Stern Tashi Walde Michael Brown Thomas Poguntke

Teaching

Sommersemester 24

Advanced algebra: Homological algebra Research seminar on higher structures

Recorded lecture courses

Higher category theory	peertube link
Algebraic Topology	peertube link

Previous teaching

Hamburg

• Lineare Algebra II (Bachelor)(Sommersemester 23)
• Research seminar on higher structures(Sommersemester 23)
• Lineare Algebra I (Bachelor)(Wintersemester 22/23)
• Research seminar on higher structures(Wintersemester 22/23)
• Algebraic Topology (Master)(Sommersemester 22)
• Research seminar on higher structures(Sommersemester 22)
• Algebraic Topology (Master) (Sommersemester 21)
• Research seminar on higher structures (Sommersemester 21)
• Introduction to higher category theory (Wintersemester 20/21)
• Differential Galois Theory (Sommersemester 20)
• Research seminar on higher structures (Sommersemester 20)
• Algebra (Bachelor) (Wintersemester 19/20)
• Research seminar on higher structures (Wintersemester 19/20)
• Research seminar on higher structures (Sommersemester 19)
• Advanced Algebra: Homological Algebra (Sommersemester 19)
• Introduction to higher category theory (Wintersemester 18/19)

Bonn

• Advanced Topics in Algebra: Vassiliev invariants and related topics (Sommersemester 18)
• Seminar: Higher Algebraic K-Theory (S4A3/Oberseminar) (Wintersemester 17/18)
• Seminar: Higher Algebra (Sommersemester 17)
• Advanced Topics in Algebra: Higher category theory (Wintersemester 16/17)
• Seminar: Noncommutative Hodge structures (Sommersemester 16)
• Seminar: Fukaya categories and related topics (Wintersemester 15/16)
• Advanced Algebra I: Homological Algebra (Sommersemester 15)
• Advanced Topics in Algebra: Hall Algebras (Wintersemester 14/15)

Oxford

• Introduction to homological algebra (Hilary Term 2014)

Yale

• Math 501: Modern Algebra II (Spring 2013)
• Math 425: Computational Algebraic Geometry (Spring 2012)
• Math 440: Introduction to Algebraic Geometry (Fall 2010)

UPenn

• Math 371: Algebra (Summer 2009)
• Math 420: Ordinary Differential Equations (Summer 2008)
• Math 412: Linear Algebra (Summer 2007)

Preprints

• Lax additivity (with M. Christ and T. Walde)
  Preprint: arXiv:2402.12251

• N-spherical functors and categorification of Euler's continuants (with M. Kapranov, V. Schechtman)
  Preprint: arXiv:2306.13350

• Complexes of stable ∞-categories (with M. Christ and T. Walde)
  Preprint: arXiv:2301.02606

Publications

• Spherical adjunctions of stable ∞-categories and the relative S-construction (with M. Kapranov, V. Schechtman, Y. Soibelman)
  Preprint: arXiv:2106.02873, accepted for publication in Math. Z.

• Perverse sheaves on Riemann surfaces as Milnor sheaves (with M. Kapranov, Y. Soibelman)
  Forum of Mathematics, Sigma, Volume 11 (2023), E92 (doi:10.1017/fms.2023.84)

• The symplectic geometry of higher Auslander algebras: Symmetric products of disks (with G. Jasso and Y. Lekili)
  Forum of Mathematics, Sigma , Volume 9 (2021), e10 (doi:10.1017/fms.2021.2)

• A relative 2-nerve (with F. Abellán García and W. H. Stern)
  Algebr. Geom. Topol. 20-6 (2020), 3147-3182 (arXiv:1910.06223)

• Generalised BGP reflection functors via the Grothendieck construction (with G. Jasso and T. Walde)
  Int. Math. Res. Not. 194 (2019) (arXiv:1901.06993)

• Relative Calabi-Yau structures II: Shifted Lagrangians in the moduli of objects (with C. Brav)
  Selecta Mathematica 27, 63 (2021) doi:10.1007/s00029-021-00642-5 (arXiv:1812.11913)

• Simplicial structures in higher Auslander-Reiten theory (with G. Jasso and T. Walde)
  Adv. Math. 355 (2019), 106762 (arXiv:1811.02461)

• A categorified Dold-Kan correspondence
  Selecta Mathematica 27, 14 (2021) (doi:10.1007/s00029-021-00618-5)

• Topological K-theory of Equivariant Singularity Categories (with M. Brown)
  Homol. Homotopy Appl., Volume 22, Number 2 (2020), 1-29 (arXiv:1611.01931)

• Relative Calabi-Yau structures (with C. Brav)
  Compos. Math. 155, Issue 2 (2019), 372-412 (arXiv:1606.00619)

• A¹-homotopy invariants of topological Fukaya categories of surfaces
  Compos. Math. 153, Issue 8 (2017), 1673–1705 (arXiv:1505.06941)

• Higher categorical aspects of Hall algebras
  Birkhäuser, Advanced Courses in Mathematics, CRM, ISBN 978-3-319-70157-8 (arXiv:1505.06940)

• Crossed simplicial groups and structured surfaces (with M. Kapranov)
  Stacks and categories in geometry, topology, and algebra, 37–110, Contemp. Math., 643, Amer. Math. Soc., Providence, RI, 2015 (arXiv:1403.5799)

• Triangulated surfaces in triangulated categories (with M. Kapranov)
  J. Eur. Math. Soc. (JEMS), Volume 20, Issue 6, 2018, pp. 1473–1524 (arXiv:1306.2545)

• Higher Segal Spaces (with M. Kapranov)
  Springer, Lecture Notes in Mathematics, Volume 2244 (2019) (arXiv:1212.3563)

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

• The Kapustin-Li formula revisited (with D. Murfet)
  Adv. Math. 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)

Editorial Duties

Abhandlungen aus dem mathematischen Seminar der Universität Hamburg	Managing editor
Applied Categorical Structures	Editor

Public lectures

• Siegerehrung der Regionalrunde der Mathematik-Olympiade 2016
  Title:Sightseeing im Hyperraum
  

• HCM Schülerinnenwoche 2016
  Title:Mit Euler zur Alhambra: Symmetrie in der Ebene
  

• Bonner Hochschultage 2015
  Title:Was ist Symmetrie?