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Thesis details
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Homotopy algebry ve vyšších kalibračnich teoriích
Thesis title in Czech: Homotopy algebry ve vyšších kalibračnich teoriích
Thesis title in English: Homotopy algebras in higher gauge theories
Key words: Supergeometrie, homotopy algebry, vyšší kalibračni teorie, Penrosova-Wardova transformace, brane scan
English key words: Supergeometry, homotopy algebras, higher gauge theories, Penrose-Ward transform, brane scan
Academic year of topic announcement: 2016/2017
Thesis type: dissertation
Thesis language:
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: 22.09.2017
Date of assignment: 22.09.2017
Confirmed by Study dept. on: 03.10.2017
Guidelines
The thesis will be devoted to a study of higher gauge theories using the methods of supergeometry, simplicial homotopy theory and homotopy algebras.
Recently, a general formulation of higher gauge theory, homotopy algebras and higher Penrose transform have been formulated and applied to the geometry of 5-branes in Ref. 1.
Also for general super p-branes, their geometry is naturally formulated using of (super) homotopy algebras in Ref 3. The goal will be extend the general methods of Ref. 1 to super p-branes.
References
1. Branislav Jurco, Christian Saemann, Martin Wolf, Higher Groupoid Bundles, Higher Spaces, and Self-Dual Tensor Field Equations, Fortschr. Phys. 64, 674-717 (2016)

2. Branislav Jurco, Christian Saemann, Martin Wolf, Semistrict Higher Gauge Theory, JHEP 04 (2015) 087

3. Domenico Fiorenza, Hisham Sati, Urs Schreiber, Super Lie n n-algebra extensions, higher WZW models and super p-branes with tensor multiplet fields, International Journal of Geometric Methods in

Modern Physics,Volume 12, Issue 02 (2015) 1550018 (35 pages)

4. https://ncatlab.org/nlab/show/geometry+of+physics+--+supergeometry+and+superphysics

5. Leonardo Castellani, Riccardo D'Auria, Pietro Fré, Supergravity and Superstrings - A Geometric Perspective, World Scientific (1991)
 
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