Geometrie symplektických gradovaných variet a jejich morfismů
| Thesis title in Czech: | Geometrie symplektických gradovaných variet a jejich morfismů |
|---|---|
| Thesis title in English: | Geometry od Symplectic Graded Manifolds and their Morphisms |
| Key words: | Courantovy algebroidy|NQP variety|BV|symplektické gradované variety |
| English key words: | Courant algebroids|NQP manifolds|BV|symplectic graded manifolds |
| Academic year of topic announcement: | 2021/2022 |
| Thesis type: | diploma thesis |
| 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: | 15.07.2021 |
| Date of assignment: | 15.07.2021 |
| Confirmed by Study dept. on: | 02.08.2021 |
| Date and time of defence: | 08.09.2021 10:00 |
| Date of electronic submission: | 27.07.2021 |
| Date of submission of printed version: | 27.07.2021 |
| Date of proceeded defence: | 08.09.2021 |
| Opponents: | Mark Bugden, Ph.D. |
| Guidelines |
| In the course of last two decades intimate relationships between graded manifolds, Courant algebroids and the geometry of Batalin-Vilkovisky quantization have been brought to light. The first task of this master thesis is to provide a sheaf-theoretic overview of the theory of symplectic differential non-negatively graded manifolds. A special subclass of these can be identified with Courant algebroids. Another task is to introduce a suitable category of symplectic differential non-negatively graded manifolds which subsumes generalized Dirac correspondences of Courant algebroids — in the spirit of Weinstein's symplectic category — and provides a categorical interpretation of the above mentioned identification. |
| References |
| D. Roytenberg, Courant algebroids, derived brackets and even symplectic supermanifolds, UC Berkeley Ph.D. thesis, arXiv:math/9910078
M. Alexandrov, M. Kontsevich, A. Schwarz, O. Zaboronsky, The geometry of the master equation and topological quantum field theory, Int. J. Modern Phys. A 12(7):1405–1429, 1997 (arXiv:hep-th/9502010) P. Ševera, Some title containing the words "homotopy" and "symplectic", e.g. this one, arXiv:0105080 A. Weinstein, Symplectic Categories, proceedings of Geometry Summer School, Lisbon, July 2009 (arXiv:0911.4133) J. Vysoky, Hitchhiker's Guide to Courant Algebroid Relations, arXiv:1910.05347 |