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Lukas Jannik Woike

I am a PhD student in Mathematics funded by the Research Training Group 1670 "Mathematics Inspired by String Theory and QFT" at the University of Hamburg.
My advisor is Christoph Schweigert.

Research interests

• Topological Field Theories, Monoidal Categories and Algebraic Topology.
  More specifically: Extended equivariant topological field theories and their orbifoldization, homotopical analogues of equivariant topological field theories.
• Homotopy Theory and Operads.
  More specifically: An operadic formulation of homotopy coherent algebraic quantum field theories and their local-to-global constructions.

Publications and Preprints

[9] The Little Bundles Operad. Joint with Lukas Müller. arXiv:1901.04850 [math.AT]

[8] Equivariant Higher Hochschild Homology and Topological Field Theories. Joint with Lukas Müller. Accepted for publication in Homology, Homotopy and Applications. arxiv.org/abs/1809.06695 [math.AT]

[7] Homotopy theory of algebraic quantum field theories. Joint with Marco Benini and Alexander Schenkel. Letters in Mathematical Physics (2019). arXiv:1805.08795 [math-ph]

[6] Parallel Transport of Higher Flat Gerbes as an Extended Homotopy Quantum Field Theory. Joint with Lukas Müller. arXiv:1802.10455 [math.QA]

[5] Involutive categories, colored ∗-operads and quantum field theory. Joint with Marco Benini and Alexander Schenkel. Theory and Applications of Categories, Vol. 34, 2019, No. 2, pp 13-57. arXiv:1802.09555 [math.CT]

[4] Extended Homotopy Quantum Field Theories and their Orbifoldization. Joint with Christoph Schweigert. arXiv:1802.08512 [math.QA]

[3] A Parallel Section Functor for 2-Vector Bundles. Joint with Christoph Schweigert. Theory and Applications of Categories, Vol. 33, 2018, No. 23, pp 644-690. arXiv:1711.08639 [math.CT]

[2] Operads for algebraic quantum field theory. Joint with Marco Benini and Alexander Schenkel. arXiv:1709.08657 [math-ph]

[1] Orbifold Construction for Topological Field Theories. Joint with Christoph Schweigert. Journal of Pure and Applied Algebra 223 (2019) 1167–1192. arXiv:1705.05171 [math.QA]

Talks

9. Derived modular functors. Topology Seminar, University of Edinburgh, March 2019.

8. Homotopy theory of algebraic quantum field theories. Séminaire de l'équipe Topologie Algébrique, Université Paris 13, November 2018.

7. Homotopy theory of algebraic quantum field theories. Séminaire de Topologie, Université Paris Diderot, November 2018.

6. Algebraic quantum field theories - Interpolating between non-commutativity and commutativity. Bayrischzell Workshop On Noncommutativity and Physics: Hopf algebras in Noncommutative Geometry, Bayrischzell, April 2018.

5. Operads and Homotopy Theory in Algebraic Quantum Field Theory. EMPG Seminar, Heriot-Watt University Edinburgh, March 2018.

4. TFT Perspective on Orbifoldization. Workshop on Tensor categories, Hopf algebras and quantum groups, Marburg, January 2018.

3. Orbifold Construction for Topological Field Theories. Universität Greifswald, Seminar on Algebraic Methods in Analysis, June 2017.

2. Orbifold Construction for Topological Field Theories. University of Nottingham, Mathematical Physics Seminar, June 2017.

1. Orbifold Construction for Topological Field Theories. Université Lille 1, Topology Seminar, June 2017.

Contact

Department of Mathematics Section Algebra and Number Theory Bundesstraße 55 (Geomatikum) 20146 Hamburg

Room 1519 Tel.: +49 40 42838 9355 E-Mail: lukas.jannik.woike (at) uni-hamburg.de