Higher Algebraic and Geometric Structures of Quantum Field Theory and String Theory

• Thesis title in Czech: Vyšší algebraické a geometrické struktury kvantové teorie pole a strunové teorie
• Thesis title in English: Higher Algebraic and Geometric Structures of Quantum Field Theory and String Theory
• 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: 01.03.2022
• Date of assignment: 01.03.2022
• Confirmed by Study dept. on: 01.03.2022
• Advisors: Jan Vysoký

Guidelines

Higher and generalized structures are at the heart of, e.g., modern homological algebra, algebraic topology and differential geometry. Recently they found profound applications in quantum theory. Its many facets and developments have widely influenced both physics and mathematics. The PhD thesis will focus on different mathematical aspects of higher and generalized structures inspired by and applied to quantum field theory, string and more generally M-theory.

References

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,

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

and the relevant references in these works