Lukas Woike

Welcome to the mathematical website of Lukas Woike

Since September 2022, I am a professeur junior at the Université Bourgogne Europe in Dijon (formerly Université de Bourgogne), more specifically at the Institut de Mathématiques de Bourgogne. I am affiliated with the research groups « Géométrie, Algèbre, Dynamique et Topologie » and « Mathématique-Physique ».

From October 2020 to August 2022, I was a postdoc at the University of Copenhagen, where my mentor was Nathalie Wahl.

From January 2022 to August 2022, my position in Copenhagen was supported by a Horizon 2020 Marie Skłodowska-Curie Fellowship of the European Union. The project has the number 101022691 and was concerned with a differential graded Verlinde formula and its connection to the Deligne's E2-structure on the Hochschild complex.

Before I obtained my doctoral degree from the University of Hamburg under the supervision of Christoph Schweigert. My doctoral studies were supported by the Research Training Group 1670 of the DFG.

My research lies at the intersection of algebra, topology and mathematical physics and is often concerned with topological field theories in some shape or form. More specifically, my interests are:

  • topological field theories in dimension three;
  • modular functors (systems of mapping class group representations), in particular those built from non-semisimple representation categories;
  • topological cyclic and modular operads, in particular the operads of little disks, handlebodies or surfaces;
  • factorization homology;
  • higher algebraic structures in the homological algebra of non-semisimple representation categories, in particular differential graded generalizations of modular functors and topological field theories;
  • the significance of all the things above in conformal field theory.
My email address is username (at) u-bourgogne.fr with the username being firstname.lastname.

Journées de Topologie Quantique

With Adrien Brochier, Renaud Detcherry and Emmanuel Wagner (and formerly Gwénaël Massuyeau), I am organizing the Journées de topologie quantique, a one-day seminar taking place most likely every few months; it will be alternating between Paris and Dijon (which are one and a half hours apart by TGV). The seminar features three talks on quantum topology (interpreted broadly) over the course of one day.

Book project

With Jürgen Fuchs and Christoph Schweigert, I have written a textbook entitled "A first course in topological field theory". It has been accepted for publication by the American Mathematical Society in their University Lecture Series and will hopefully soon be available. Feel free to contact me about more information.

Me

Image source: private.

Preprints

  1. Modular functors from conformal blocks of rational vertex operator algebras. With Chiara Damiolini. arxiv.org/abs/2507.05845
  2. Admissible Skein Modules and Ansular Functors: A Comparison. With Lukas Müller. arxiv.org/abs/2409.17047
  3. The Lyubashenko Modular Functor for Drinfeld Centers via Non-Semisimple String-Nets. With Lukas Müller, Christoph Schweigert and Yang Yang. arxiv.org/abs/2312.14010
  4. A Classification of Modular Functors via Factorization Homology. With Adrien Brochier. arxiv.org/abs/2212.11259

Publications (accepted, in press, published online and/or in print, ...)

  1. The Cyclic and Modular Microcosm Principle in Quantum Topology. Accepted for publication in Canad. J. Math. arxiv.org/abs/2408.02644
  2. The Dehn Twist Action for Quantum Representations of Mapping Class Groups. With Lukas Müller. Accepted for publication in J. Top. arxiv.org/abs/2311.160200
  3. Categorified Open Topological Field Theories. With Lukas Müller. Accepted for publication in Proc. Amer. Math. Soc. arxiv.org/abs/2406.11605
  4. The distinguished invertible object as ribbon dualizing object in the Drinfeld center. With Lukas Müller. Selecta Math. New Ser. 30:98, 2024. arxiv.org/abs/2212.07910
  5. Homotopy Invariants of Braided Commutative Algebras and the Deligne Conjecture for Finite Tensor Categories. With Christoph Schweigert. Adv. Math. 422:109006, 2023. arXiv.org/abs/2204.09018
  6. Classification of Consistent Systems of Handlebody Group Representations. With Lukas Müller. Int. Math. Res. Not. 2024(6):4767-4803, 2024. arXiv.org/abs/2201.07542
  7. The Diffeomorphism Group of the Solid Closed Torus and Hochschild Homology. With Lukas Müller. Proc. Amer. Math. Soc. 151(6):2311-2324, 2023. arXiv/abs/2201.03920
  8. The differential graded Verlinde Formula and the Deligne Conjecture. With Christoph Schweigert. Proc. London Math. Soc. 126(6):1811-1841, 2023. arxiv.org/abs/2105.01596
  9. The Trace Field Theory of a Finite Tensor Category. With Christoph Schweigert. Alg. Rep. Theory 26:1931-1949, 2023. arxiv.org/abs/2103.15772
  10. Cyclic framed little disks algebras, Grothendieck-Verdier duality and handlebody group representations. With Lukas Müller. Quart. J. Math. 74(1):163-245, 2023. arxiv.org/abs/2010.10229
  11. Homotopy Coherent Mapping Class Group Actions and Excision for Hochschild Complexes of Modular Categories. With Christoph Schweigert. Adv. Math. 386:107814, 2021. arxiv.org/abs/2004.14343
  12. Dimensional Reduction, Extended Topological Field Theories and Orbifoldization. With Lukas Müller. Bull. London Math. Soc. 53(2):392-403, 2020. arxiv.org/abs/2004.04689
  13. Categorification of algebraic quantum field theories. With Marco Benini, Marco Perin and Alexander Schenkel. Lett. Math. Phys. 111(35), 2021. arxiv.org/abs/2003.13713
  14. The Hochschild Complex of a Finite Tensor Category. With Christoph Schweigert. Algebr. Geom. Top. 21(7):3689-3734, 2021. arxiv.org/abs/1910.00559
  15. The Little Bundles Operad. With Lukas Müller. Algebr. Geom. Top. 20(4):2029-2070, 2020. arxiv.org/abs/1901.04850
  16. Equivariant Higher Hochschild Homology and Topological Field Theories. With Lukas Müller. Homology Homotopy Appl. 22(1):27-54, 2020. arxiv.org/abs/1809.06695
  17. Homotopy theory of algebraic quantum field theories. With Marco Benini and Alexander Schenkel. Lett. Math. Phys. 109:1487-1532, 2019. arxiv.org/abs/1805.08795
  18. Parallel Transport of Higher Flat Gerbes as an Extended Homotopy Quantum Field Theory. With Lukas Müller. J. Homotopy Relat. Str. 15:113-142, 2020.arxiv.org/abs/1802.10455
  19. Extended Homotopy Quantum Field Theories and their Orbifoldization. With Christoph Schweigert. J. Pure Appl. Algebra 224(4):106213, 2020. arxiv.org/abs/1802.08512
  20. Involutive categories, colored ∗-operads and quantum field theory. With Marco Benini and Alexander Schenkel. Theory Appl. Categ. 34(2):13-57, 2019. arxiv.org/abs/1802.09555
  21. A Parallel Section Functor for 2-Vector Bundles. With Christoph Schweigert. Theory Appl. Categ. 33(23):644-690, 2018. arxiv.org/abs/1711.08639
  22. Operads for algebraic quantum field theory. With Marco Benini and Alexander Schenkel. Commun. Contemp. Math. 23(02):2050007, 2021.arxiv.org/abs/1709.08657
  23. Orbifold Construction for Topological Field Theories. With Christoph Schweigert. J. Pure Appl. Algebra 223:1167-1192, 2019. arxiv.org/abs/1705.05171

Institut de Mathématiques de Bourgogne
UMR 7586 CNRS
Université Bourgogne Europe
Faculté des Sciences Mirande
9 Avenue Alain Savary
F-21000 Dijon

Me Me Me

Me