Generalised geometry 2 - NMAG598

• Title: Generalised geometry 2
• Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
• Faculty: Faculty of Mathematics and Physics
• Actual: from 2025
• Semester: summer
• E-Credits: 3
• Hours per week, examination: summer s.:2/0, Ex [HT]
• Capacity: unlimited
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: taught
• Language: English
• Teaching methods: full-time
• Guarantor: Mgr. Fridrich Valach, Ph.D.
• Teacher(s): Mgr. Fridrich Valach, Ph.D.
• Class: M Mgr. MSTR; M Mgr. MSTR > Volitelné
• Classification: Mathematics > Geometry

Annotation

English

Building on the course Generalised geometry, we will develop further aspects of the theory of Courant algebroids and study the applications of these structures in the context of string theory, its dualities, and the corresponding supergravity. In particular we will introduce the foundational concepts in generalised Riemannian geometry

Last update: Fatková Tereza, Ing. (02.01.2026)

Czech

V návaznosti na kurz Zobecněná geometrie rozvineme další aspekty teorie Courantových algebroidů a budeme studovat aplikace těchto struktur v kontextu teorie strun, jejích dualit a odpovídající supergravitace. Mimo jiné představíme základní koncepty zobecněné Riemannovy geometrie

Last update: Fatková Tereza, Ing. (02.01.2026)

Course completion requirements

prezentace/ústní skouška

Last update: Valach Fridrich, Mgr., Ph.D. (25.01.2026)

Literature

M. Gualtieri: Generalized Complex Geometry, Oxford University DPhil thesis (2004), https://arxiv.org/abs/math/0401221

M. Garcia-Fernandez, J. Streets, Generalized Ricci Flow: Generalized Ricci flow, Vol. 76, American Mathematical Soc., 2021.

Last update: Valach Fridrich, Mgr., Ph.D. (25.01.2026)

Teaching methods

blackboard lectures

Last update: Valach Fridrich, Mgr., Ph.D. (25.01.2026)

Syllabus

Preliminary schedule:

• Generalised Riemannian geometry: generalised metrics, connections and divergences, generalised curvature tensors and Einstein-Hilbert action, generalised Ricci flow and its relation to sigma models

• Courant algebroid reductions and pullbacks, Poisson-Lie T-duality

• Spinors, Dirac operators, and supergravity

Last update: Valach Fridrich, Mgr., Ph.D. (25.01.2026)