Některá témata ve vyšších algebraických a geometrických strukturách
| Název práce v češtině: | Některá témata ve vyšších algebraických a geometrických strukturách |
|---|---|
| Název v anglickém jazyce: | Some topics in higher algebraic and gemetric structures |
| Akademický rok vypsání: | 2023/2024 |
| Typ práce: | disertační práce |
| Jazyk práce: | čeština |
| Ústav: | Matematický ústav UK (32-MUUK) |
| Vedoucí / školitel: | prof. Ing. Branislav Jurčo, CSc., DSc. |
| Řešitel: | skrytý - zadáno a potvrzeno stud. odd. |
| Datum přihlášení: | 19.09.2023 |
| Datum zadání: | 19.09.2023 |
| Datum potvrzení stud. oddělením: | 05.10.2023 |
| Konzultanti: | Jan Vysoký |
| Zásady pro vypracování |
| Recently, methods of modern homological algebra, algebraic topology and differential geometry found profound applications in quantum theory. Many facets and developments of the related higher algebraic and geometric structuresIts have widely influenced both physics and mathematics. The PhD thesis will focus on different mathematical aspects of higher and generalized structures inspired by string and more generally M-theory, in particular Courant algebroids and their modifications and/or generalizations. |
| Seznam odborné literatury |
| Branislav Jurco, Christian Saemann, Martin Wolf, Higher Groupoid Bundles, Higher Spaces, and Self-Dual Tensor Field Equations, Fortschr. Phys. 64, 674-717 (2016)
Kevin Costello, Renormalization and Effective Field Theory Leron Borsten, Branislav Jurco, Hyungrok Kim, Tommaso Macrelli, Christian Saemann, Martin Wolf, Double Copy from Homotopy Algebras, Fortschr. Phys. 69 (2021) 2100075, P. Mnev, Quantum Field Theory: Batalin-vilkovisky Formalism and Its Applications (University Lecture Series, Band 72), AMS 2019 Branislav Jurco, Lorenzo Raspollini, Christian Saemann, Martin Wolf, L∞-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism, Phys. 67 (2019) 1900025 Branislav Jurco, Jan Vysoky, Poisson-Lie T-duality of String Effective Actions: A New Approach to the Dilaton Puzzle, arXiv:1708.04079 M. Doubek, B. Jurco, M. Markl, I. Sachs, Algebraic structure of quantum field theory M. Gualtieri, Generalized comlex geoemtry, Oxford University DPhil thesis, 2004 J. Vysoky, Graded generalized geometry, Journal of Geometry and Physics 182, 104683, 2022 B. Jurco, F. Moucka, J Vysoky, Palatini Variation in Generalized Geometry and String Effective Actions, arXiv:2211.09138 J Vysoky, Global theory of graded manifolds, Reviews in Mathematical Physics 34 (10), 2250035 and the relevant references in these works |