Vyšší a zobecněné struktury v matematické fyzice
| Název práce v češtině: | Vyšší a zobecněné struktury v matematické fyzice |
|---|---|
| Název v anglickém jazyce: | Higher and Generalized Structures in Mathematical Physics |
| Klíčová slova: | BV-kvantovani|homotopicky transfer|dg-variety|zobecena geometrie |
| Klíčová slova anglicky: | BV-quantization|homotopy tenasfer|dg-manifolds|generalized geometry |
| Akademický rok vypsání: | 2022/2023 |
| Typ práce: | diplomová práce |
| Jazyk práce: | |
| Ústav: | Matematický ústav UK (32-MUUK) |
| Vedoucí / školitel: | prof. Ing. Branislav Jurčo, CSc., DSc. |
| Řešitel: | skrytý - zadáno vedoucím/školitelem |
| Datum přihlášení: | 14.09.2022 |
| Datum zadání: | 14.09.2022 |
| Zásady pro vypracování |
| 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. |
| Seznam odborné literatury |
| 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 |