Geometry and Topology
in Physics 2023
Lecturer: Daniel Galviz
Content
Basic definitions & Topological spaces
Manifolds
Differential forms
de Rham cohomology
Riemannian Geometry
Homology and cohomology groups
Fundamental groups and Homotopy groups
Lie groups and Lie algebras
Fibre bundles and Principal G-bundles
Complex Geometry
Characteristic classes
Index Theorem
Chern-Simons theory
Moduli spaces
The course is evaluated with assignments (60%), seminars (10%) and a final exam (30%).
Applications are now closed
Lecture Notes
Moduli spaces
Guest Speakers
Nikita Nekrasov [The Count of Instantons] [Slides]
Johanna Knapp [Gauged linear sigma models and Calabi-Yaus] [Slides]
Mauricio Romo [Algebraic Geometry and String Theory] [Slides]
Anamaría Font [Old and new from Heterotic Strings] [Slides]
Xenia de la Ossa [Reflections on Mirror Symmetry] [Slides]
Alessandro Tomasiello [Toric Geometry for String Theory] [Slides]
LITERATURE
Differential Geometry
John Lee. Introduction to Smooth Manifolds.
Loring W. Tu. An Introduction to Manifolds.Riemannian Geometry
John Lee. Introduction to Riemannian Manifolds.Topology
Allen Hatcher. Algebraic Topology.Complex Geometry
Daniel Huybrechts. Complex Geometry: An Introduction.
Phillip Griffiths and Joseph Harris. Principles of Algebraic Geometry.Math in Physics
Mikio Nakahara. Geometry, Topology and Physics.
Satoshi Nawata. Differential Geometry and Topology in Physics.
Charles Nash and Siddhartha Sen. Topology and Geometry for Physicists.
Alessandro Tomasiello. Geometry of String Theory Compactifications.
Frederic Schuller. Video Lectures: Geometrical Anatomy of Theoretical Physics.
successfully passed students
Edgar Condori 🇵🇪(University of Guanajuato, MX)
Krystifer Campos🇨🇴
(University of Valle, CO)
Cristian Gallegos🇲🇽
(Autonomous University of Nuevo León, MX)
Jean Gómez 🇻🇪
(University Simón Bolı́var , VE)
Allan Hurtado 🇬🇹
(University of San Carlos of Guatemala, GT)
Victor Lopez 🇲🇽
(University of Guanajuato, MX)
Cristhian Martinez🇨🇴
(The University of Valle, CO)
Diego Suárez 🇵🇪
(National University of Engineering, PE)
Steven Perlaza🇨🇴
(The University of Valle, CO)
Genivaldo Pinheiro 🇧🇷
(Federal University of Ceará, BR)
Román Rodríguez 🇲🇽
(Autonomous University of Nuevo León, MX)
William salazar 🇨🇴
(The University of Valle, CO)
Guest SPEAKERs
Prof. Nikita Nekrasov
(Stony Brook University
Simons Center for Geometry and Physics, USA)
Prof. Anamaría Font
(Central Univ. of Venezuela & Max-Planck Institute, DE)
Prof. Nicolai Reshetikhin
(Tsinghua University,
UC Berkeley)
Prof. Xenia de la Ossa
(University of Oxford, UK)
Prof. Alessandro Tomasiello
(University of Milano-Bicocca, IT)
Prof. Mauricio Romo
(Tsinghua University, CN)
Teaching assistanTS
(Johannes Gutenberg University of Mainz, DE)
(Pure Mathematics University of Waterloo, CA)
