Vyšší a zobecněné struktury v matematické fyzice
| Thesis title in Czech: | Vyšší a zobecněné struktury v matematické fyzice |
|---|---|
| Thesis title in English: | Higher and Generalized Structures in Mathematical Physics |
| Key words: | BV-kvantovani|homotopicky transfer|dg-variety|zobecena geometrie |
| English key words: | BV-quantization|homotopy tenasfer|dg-manifolds|generalized geometry |
| Academic year of topic announcement: | 2022/2023 |
| Thesis type: | diploma thesis |
| Thesis language: | |
| Department: | Mathematical Institute of Charles University (32-MUUK) |
| Supervisor: | prof. Ing. Branislav Jurčo, CSc., DSc. |
| Author: | hidden - assigned by the advisor |
| Date of registration: | 14.09.2022 |
| Date of assignment: | 14.09.2022 |
| 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 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 |