phys250

Physics 250: Topics Course / Learning Seminar
Mathematical Methods of Physics

Tuesday 12:30 - 2:00pm
Broida 3302

Instructor: Sergei Gukov

The setting will be a bit less formal than in a typical graduate course and will allow a lot of room for questions, discussions, and choice of topics to be covered. A possible list of topics may include: complex manifolds, vector bundles, elements of algebraic topology and representation theory, including characters, weights, roots, Dynkin diagrams, classical Lie groups, and their use in physics. Both physics and math graduate students are invited!

Textbooks:

M. Nakahara, Geometry, Topology and Physics (2003)
T. Frankel, The Geometry of Physics: An Introduction (1999)
H. Georgi, Lie Algebras in Particle Physics (1999)
W. Fulton, J. Harris, Representation Theory. A First Course (1991)
V.S. Varadarajan, Lie Groups, Lie Algebras, and Their Representation (1984)
W. Massey, A Basic Course in Algebraic Topology (1997)
R. Bott, L. Tu, Differential Forms in Algebraic Topology (1995)
A. Hatcher, Algebraic Topology (2001)
R.O. Wells, Differential Analysis on Complex Manifolds (1986)

Schedule
Week	Topic
1	Organizational meeting / Introduction
2	Lie groups and Lie algebras
3	Representations
4	Roots and weights
5	Classification of root systems
6	Representations revisited
7	Coroots and coweights / The fundamental group
8	Homology and cohomology
9	Winter break
10	Singular homology
11	Applications
12	Complex manifolds
13	Symplectic and Kahler geometry
14	Geometry of gauge fields
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