Homepages

(hier geht es zur ggf. vollständigeren Homepage im alten Layout)
(this way to the possibly more complete Homepage in the old layout)

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

Algebraic topology, representation theory, in particular topological field theory.

My PhD project is concerned with

• extended equivariant topological field theories and their orbifoldization as well as higher-categorical aspects of equivariant topological field theories,
• applications of homotopical algebra (in particular operads) to non-semisimple representation categories leading to derived modular functors.

Publications

[8] The Little Bundles Operad. Joint with Lukas Müller. 2019. Accepted for publication in Algebr. Geom. Top. arXiv:1901.04850 [math.AT]

[7] Equivariant Higher Hochschild Homology and Topological Field Theories. Joint with Lukas Müller. Homology Homotopy Appl. 22(1):27-54, 2020. arxiv.org/abs/1809.06695 [math.AT]

[6] Homotopy theory of algebraic quantum field theories. Joint with Marco Benini and Alexander Schenkel. Lett. Math. Phys. 109:1487-1532, 2019. arXiv:1805.08795 [math-ph]

[5] Parallel Transport of Higher Flat Gerbes as an Extended Homotopy Quantum Field Theory. Joint with Lukas Müller. J. Homotopy Relat. Str. (Online first) arXiv:1802.10455 [math.QA]

[4] Extended Homotopy Quantum Field Theories and their Orbifoldization. Joint with Christoph Schweigert. J. Pure Appl. Algebra. (Online first) arXiv:1802.08512 [math.QA]

[3] Involutive categories, colored ∗-operads and quantum field theory. Joint with Marco Benini and Alexander Schenkel. Theory Appl. Categ. 34(2):13-57, 2019. arXiv:1802.09555 [math.CT]

[2] A Parallel Section Functor for 2-Vector Bundles. Joint with Christoph Schweigert. Theory Appl. Categ. 33(23):644-690, 2018. arXiv:1711.08639 [math.CT]

[1] Orbifold Construction for Topological Field Theories. Joint with Christoph Schweigert. J. Pure Appl. Algebra 223:1167-1192, 2019. arXiv:1705.05171 [math.QA]

Preprints

[2] The Hochschild Complex of a Finite Tensor Category. Joint with Christoph Schweigert. 2019. arXiv:1910.00559 [math.QA]

[1] Operads for algebraic quantum field theory. Joint with Marco Benini and Alexander Schenkel. 2017. arXiv:1709.08657 [math-ph]

Talks

12. The Hochschild Complex of a Finite Tensor Category. Memorial University Newfoundland, November 2019.

11. Boundary Conditions and the Swiss-Cheese Operad. Workshop on Defects in topological and conformal field theory, King's College London, June 2019.

10. Derived modular functors. Topology Seminar, University of Oxford, June 2019.

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