Higher and Generalized Structures in Mathematical Physics

• Thesis title in Czech: Vyšší a zobecněné struktury v matematické fyzice
• Thesis title in English: Higher and Generalized Structures in Mathematical Physics
• Key words: homtopické algebry|BV-kvantování|zobecněná symplektická a komplexní geometrie|dg variety|homtopický transfér
• English key words: homotopy algebras|BV-quantization|dg manifolds|generalized symplectic and complex geometry|homtopy transfer
• Academic year of topic announcement: 2021/2022
• Thesis type: dissertation
• Thesis language: angličtina
• Department: Mathematical Institute of Charles University (32-MUUK)
• Supervisor: prof. Ing. Branislav Jurčo, CSc., DSc.
• Author: hidden - assigned and confirmed by the Study Dept.
• Date of registration: 22.09.2022
• Date of assignment: 22.09.2022
• Confirmed by Study dept. on: 22.09.2022

Guidelines

Higher and generalized structures play a central role in contemporary geometry and mathematical physics. The tools and perspectives they provide have widely influenced both purely mathematical topics including homological algebra, homotopy theory, differential geometry and category theory or modern fields of physics such as quantum field theory or string theory. The PhD thesis will focus on the interactions between those topics and mathematical aspects of higher structures as they arise in mathematical physics.

References

Tom Leinster, Ed., Higher Operads, Higher Categories, Cambridge Univ. Press, 2004



Kevin Costello, Renormalization and Effective Field Theory



Branislav Jurco, Lorenzo Raspollini, Christian Saemann, Martin Wolf, L∞-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism, Phys. 67 (2019) 1900025



Bunk, Severin. (2021). Gerbes in Geometry, Field Theory, and Quantisation. Complex Manifolds. 8. 150-182. 10.1515/coma-2020-0112.



Branislav Jurco, Christian Saemann, Martin Wolf, Higher Groupoid Bundles, Higher Spaces, and Self-Dual Tensor Field Equations, Fortschr. Phys. 64, 674-717 (2016)



Baez, John & Huerta, John. (2010). An Invitation to Higher Gauge Theory. General Relativity and Gravitation. 43. 10.1007/s10714-010-1070-9.



Branislav Jurco, Christian Saemann, Martin Wolf, Semistrict Higher Gauge Theory, JHEP 04 (2015) 087



M. Doubek, B. Jurco, M. Markl, I. Sachs, Algebraic Structure of String Field Theory