Geometry and Topology in Physics (Fall 2025)

Part 1: Basic Ingredients

Lecture 1: Topological Thinking

Lecture 2: Topological/Differentiable/Smooth Manifolds

Lecture 3: The Tangent Space

Lecture 4: Tensors and Differential Forms

Lecture 5: Exterior Derivative, Integration, and Hodge Star

Part 2: Continuous Symmetry

Lecture 6: Lie Groups (by Masih Ansari)

Lecture 7: Lie Algebras (by Mahdiyar Niaei)

Lecture 8: Representations of Lie Groups and Lie Algebras

Lectures 9&10: Lorentz and Poincare Groups: an Introduction to Special Relativity

Lecture 11: Representations of the Lorentz and Poincare Groups: Fields and Particles

Part 3: Differential Geometry

Lecture 12: Introduction to Vector and Fiber Bundles (by Bamdad Torabi)

Lecture 13: Principal and Associated Bundles

Lecture 14: Connections on Principal and Associated Bundles (by Borna Khodabandeh)

Lecture 15: Parallel Transport and Curvature (by Arshia Jafari)

Lecture 16: Berry Phase as Holonomy of a Principal U(1) Bundle (by Alireza Goudarzi)

Lecture 17: Electromagnetism, Yang--Mills Theory, and the Standard Model

Lecture 18: Riemannian Geometry (by Sarina Mardanian)

Lecture 19: General Relativity

Part 4: Topology

Lectures 20&21: Homotopy and the Fundamental Group (by Niki Hasani)

Lecture 22: Homology Groups (by Mahdi Hajary)

Lecture 23: Cohomology and deRham's Theorem (by Amir Mohammadi)

Lecture 24: Exact Sequences and Poincare Duality

Lecture 25: TBA