Prof. Dr. Tobias Dyckerhoff
- Address
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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 2395-25152
- tobias.dyckerhoff AT uni-hamburg.de
- Public Key
- public.pgp
-
- @tobias.dyckerhoff:matrix.math.uni-hamburg.de
-
- tube.octaplex.net
About me
I am a mathematician at the University of Hamburg affiliated with:
Research interests
My research is concerned with higher structures in algebra and geometry.
Events
Visit our joint event calendar containing events of interest to the groups "Analysis and Differential Geometry (AD)" and "Algebra and Number Theory (AZ)".
Workshop on higher categorical methods in algebra and geometry, March 22–24, 2023 (Hamburg). Website
Research group
Teaching
Previous teaching
Hamburg
- Advanced algebra: Homological algebra (Sommersemester 24)
- Research seminar on higher structures (Sommersemester 24)
- 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)
Recorded lecture courses
Preprints
- Hypersheaves and bases (with T. Heine, S. Schneider) arXiv:2506.14007
- Perverse schobers of Coxeter type A (with P. Wedrich) arXiv:2504.08496
- Complexes of stable ∞-categories (with M. Christ, T. Walde) arXiv:2301.02606
Publications
- Lax additivity (with M. Christ, T. Walde) Doc. Math. 31 (2026), no. 4, 787–853 doi:10.4171/DM/1051 , arXiv:2402.12251
- N-spherical functors and categorification of Euler’s continuants (with M. Kapranov, V. Schechtman) Math. Z. 312, 75 (2026) doi:10.1007/s00209-026-03949-1 , arXiv:2306.13350
- Cyclic polytopes, orientals, and correspondences: Some aspects of Higher Segal spaces Contemporary Mathematics 838: Higher Segal Spaces and Applications (2026), 131–158 doi:10.1090/conm/838/16739 , arXiv:2505.02051
- Spherical adjunctions of stable ∞-categories and the relative S-construction (with M. Kapranov, V. Schechtman, Y. Soibelman) Math. Z. 307, 73 (2024) doi:10.1007/s00209-024-03549-x , arXiv:2106.02873
- 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 , arXiv:2012.11388
- The symplectic geometry of higher Auslander algebras: Symmetric products of disks (with G. Jasso, Y. Lekili) Forum of Mathematics, Sigma, Volume 9 (2021), e10 doi:10.1017/fms.2021.2 , arXiv:1911.11719
- A relative 2-nerve (with F. Abellán García, W. H. Stern) Algebr. Geom. Topol. 20-6 (2020), 3147–3182 doi:10.2140/agt.2020.20.3147 , arXiv:1910.06223
- Generalised BGP reflection functors via the Grothendieck construction (with G. Jasso, T. Walde) Int. Math. Res. Not. 194 (2019) doi:10.1093/imrn/rnz194 , 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, T. Walde) Adv. Math. 355 (2019), 106762 doi:10.1016/j.aim.2019.106762 , arXiv:1811.02461
- A categorified Dold-Kan correspondence Selecta Mathematica 27, 14 (2021) doi:10.1007/s00029-021-00618-5 , arXiv:1710.08356
- Topological K-theory of Equivariant Singularity Categories (with M. Brown) Homol. Homotopy Appl., Volume 22, Number 2 (2020), 1–29 doi:10.4310/hha.2020.v22.n2.a1 , arXiv:1611.01931
- Relative Calabi-Yau structures (with C. Brav) Compos. Math. 155, Issue 2 (2019), 372–412 doi:10.1112/s0010437x19007024 , arXiv:1606.00619
- A¹-homotopy invariants of topological Fukaya categories of surfaces Compos. Math. 153, Issue 8 (2017), 1673–1705 doi:10.1112/s0010437x17007205 , arXiv:1505.06941
- Higher categorical aspects of Hall algebras Birkhäuser, Advanced Courses in Mathematics, CRM, ISBN 978-3-319-70157-8 doi:10.1007/978-3-319-70157-8_1 , 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 doi:10.1090/conm/643/12896 , arXiv:1403.5799
- Triangulated surfaces in triangulated categories (with M. Kapranov) J. Eur. Math. Soc. (JEMS), Volume 20, Issue 6, 2018, pp. 1473–1524 doi:10.4171/jems/791 , arXiv:1306.2545
- Higher Segal Spaces (with M. Kapranov) Springer, Lecture Notes in Mathematics, Volume 2244 (2019) doi:10.1007/978-3-030-27124-4 , arXiv:1212.3563
- Pushing forward matrix factorisations (with D. Murfet) Duke Math. J. Volume 162, Number 7 (2013), 1249–1311 doi:10.1215/00127094-2142641 , arXiv:1102.2957
- The Kapustin-Li formula revisited (with D. Murfet) Adv. Math. 231 (2012), pp. 1858–1885 doi:10.1016/j.aim.2012.07.021 , arXiv:1004.0687
- Compact generators in categories of matrix factorizations Duke Math. J. Volume 159, Number 2 (2011), 223–274 doi:10.1215/00127094-1415869 , arXiv:0904.4713
- The inverse problem of differential Galois theory over the field R(z) Mathematisches Forschungsinstitut Oberwolfach Report No. 26/2007 arXiv:0802.2897
Editorial duties
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?