Schaumann Gregor Dr.

• Mathematical Physics: Interpretations and conceptual Questions
• Topological Field Theories and Higher Categories
• Tensor Categories and Representations

My projects are concerned with the interplay of algebra and geometry in the areas of quantum algebra, low-dimensional topology and (higher) category theory.
In particular, I am interested in the interdisciplinary area of topological field theories (TFT) and the manifold invariants that arise from such theories.

• Supervision in Würzburg: Bachelor theses, Master theses, PhD theses
• Teaching in Würzburg
• Previous teaching: Linear Algebra for GMR-teachers candidates,  Introduction to knot theory, Topology, algebraic topology,
  elementary differential geometry, geometric mechanics, various seminars and RiGs.

1. J. Fuchs, G.S., C. Schweigert, and S. Wood. Grothendieck-Verdier
   module categories, Frobenius algebras and relative Serre functors, arXiv, 2024-05-31.
   [Abstract] [PDF]
2. G. S. Fusion quivers. arXiv:2307.09229, 2023-07-18.
   [Abstract] [PDF]
3. N. Carqueville, V. Mulevicius, R. Runkel, G. S., and D. Scherl.
   Orbifold graph tqfts. arXiv:2101.02482, 2021
   [Abstract] [PDF]
4. P Etingof. Eigenvalues of the squared antipode in finite dimensional weak
   Hopf algebras. In Tensor categories and Hopf algebras, volume 728 of Contemp.
   Math., pages 95–117. Amer. Math. Soc., Providence, RI, 2019. doi: 10.1090/
   conm/728/14657. With an appendix by G.S.

1. J. Fuchs, G. S., C. Schweigert, and S. Wood. Grothendieck-Verdier
   duality in categories of bimodules and weak module functors. Quantum Symme-
   tries: Tensor Categories, Topological Quantum Field Theories, Vertex Algebras,
   Contemporary Mathematics, AMS, 2024.
2. J. W. Barrett, C. Meusburger, and G. S. Gray categories with
   duals and their diagrams. Adv. Math., 450:Paper No. 109740, 2024-07.
3. N. Carqueville, V. Mulevicius, I. Runkel, G. S., and D. Scherl.
   Reshetikhin–Turaev TQFTs Close Under Generalised Orbifolds. Comm.
   Math. Phys., 405(10):Paper No. 242, 2024-09-17.
4. J. Fuchs, G. S., and C. Schweigert. Module Eilenberg-Watts calculus.
   In Hopf algebras, tensor categories and related topics, volume 771 of Contemp.
   Math., pages 117–136. Amer. Math. Soc., [Providence], RI, 2021.
5. J. Fuchs, G. S., and C. Schweigert. A modular functor from state
   sums for finite tensor categories and their bimodules. Theory Appl. Categ.,
   38:436–594, 2022-03-22.
6. N. Carqueville, I. Runkel, and G. S. Orbifolds of Reshetikhin-Turaev
   TQFTs. Theory Appl. Categ., 35:513–561, 2020.
7. J. Fuchs, G. S., and C. Schweigert. Eilenberg-Watts calculus for finite
   categories and a bimodule Radford s4 theorem. Transactions of the American
   Mathematical Society, 2019.
8. N. Carqueville, I. Runkel, and G. S. Orbifolds of n-dimensional
   defect TQFTs. Geom. Topol., 23(2):781–864, 2019.
9. N. Carqueville, I. Runkel, and G. S. Line and surface defects in
   Reshetikhin-Turaev TQFT. Quantum Topol., 10(3):399–439, 2019.
10. J., Fuchs, T. Gannon, G.S., C. Schweigert: The logarithmic Cardy case: Boundary states and annuli.
    Nuclear Physics B 930 (2018): 287-327.
11. J. Fuchs, C. Schweigert, G.S.: A trace for bimodule categories.
    Applied Categorical Structures, online first, DOI 10.1007/s10485– 016–9425–3, 2016.
12. N. Carqueville, C. Meusburger, and G. S.. 3-dimensional defect
    TQFTs and their tricategories. Adv. Math., 364:58, 2020-04-15.
13. G.S.: Pivotal tricategories and a categorification of inner-product modules.
    Algebras and Representation Theory 18(6):1407–1479, 2015.
14. G.S.: Traces on module categories over fusion categories.
    J. Algebra 379, 382–425, 2013.
15. S. Jansen, N. Neumaier, G.S., S. Waldmann.: Classification of invariant star products up to equivariant Morita equivalence on symplectic manifolds.
    Letters in Mathematical Physics, 100 (203-236), 2012.

G.S.: Duals in tricategories and in the tricategory of bimodule categories 
PhD-thesis, 2013.