Fachbereich Mathematik 
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Lukas Jannik Woike

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 and quantum topology, representation theory, in particular topological field theory.

My projects are 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 modular functors with values in chain complexes.

Publications

[9] The Little Bundles Operad. Joint with Lukas Müller. Algebr. Geom. Top. 20:2029-2070, 2020. arXiv:1901.04850 [math.AT]

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

[7] 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]

[6] 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]

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

[4] 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]

[3] 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]

[2] Operads for algebraic quantum field theory. Joint with Marco Benini and Alexander Schenkel. 2017. Accepted for publication in Commun. Contemp. Math. arXiv:1709.08657 [math-ph]

[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

[4] Homotopy Coherent Mapping Class Group Actions and Excision for Hochschild Complexes of Modular Categories. Joint with Christoph Schweigert. 2020. arXiv:2004.14343 [math.QA]

[3] Dimensional Reduction, Extended Topological Field Theories and Orbifoldization. Joint with Lukas Müller. 2020. arXiv:2004.04689 [math.QA]

[2] Categorification of algebraic quantum field theories. Joint with Marco Benini, Marco Perin and Alexander Schenkel. 2020. arXiv:2003.13713 [math-ph]

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

Talks

Topology Seminar, University of Stockholm/KTH, February 2020.

Topology Seminar, University of Copenhagen, January 2020.

Seminar of the group of Ulrich Bunke, Universität Regensburg, December 2019.

Arbeitsgemeinschaft Algebra, TU München, December 2019.

Seminar, Max Planck Institute for Mathematics, December 2019.

Opening workshop of the OCHoTop project at the École polytechnique fédérale de Lausanne, December 2019.

Topology seminar, Institut Montpelliérain Alexander Grothendieck, December 2019.

Algebra seminar, Memorial University Newfoundland, November 2019.

Workshop on Defects in topological and conformal field theory, King's College London, June 2019.

Topology Seminar, University of Oxford, June 2019.

Topology Seminar, University of Edinburgh, March 2019.

Séminaire de l'équipe Topologie Algébrique, Université Paris 13, November 2018.

Séminaire de Topologie, Université Paris Diderot, November 2018.

Bayrischzell Workshop On Noncommutativity and Physics: Hopf algebras in Noncommutative Geometry, Bayrischzell, April 2018.

EMPG Seminar, Heriot-Watt University Edinburgh, March 2018.

Workshop on Tensor categories, Hopf algebras and quantum groups, Marburg, January 2018.

Seminar on Algebraic Methods in Analysis, Universität Greifswald, June 2017.

Mathematical Physics Seminar, University of Nottingham, June 2017.

Topology Seminar, Université Lille 1, 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

 
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