- Topics in Representation Theory: SU(2) Representations and Their Applications
- Topics in Representation Theory: The Adjoint Representation
- Groups and Representations II: Problem Set 1 Due Wednesday, February 12
- Groups and Representations II: Problem Set 6 Due Monday, February 21
- Topics in Representation Theory: The Spinor Representation
- Modern Geometry I: Problem Set 4 Due Monday, November 29
- Lie Groups and Representations: Syllabus Fall Semester
- Modern Geometry I: Problem Set 2 Due Monday, October 18
- Groups and Representations II: Problem Set 4 Due Monday, April 16
- Quantum Field Theory for Mathematicians: Background and History
- Topics in Representation Theory: Clifford So far in this course we have given a very general theory of compact Lie
- Quantum Field Theory and Representation Theory: A Sketch
- Topics in Representation Theory: The Heisenberg Algebra
- Quantum Field Theory for Mathematicians Hamiltonian Mechanics and Symplectic Geometry
- Topics in Representation Theory: Cultural This semester we will be covering various topics in representation theory, see
- String Theory: An Evaluation Department of Mathematics, Columbia University
- Quantum Field Theory and Representation Theory
- Groups and Representations I: Problem Set 5 Due Monday, December 3
- Groups and Representations II: Problem Set 7 Due Monday, March 24
- Topics in Representation Theory: Finite Groups and Character Theory
- Topics in Representation Theory: More About the Exponential Map
- Topics in Representation Theory: SU(n), Weyl Chambers and the Diagram of a Group
- Topics in Representation Theory: The Killing Form, Reflections and Classification of Root
- Topics in Representation Theory: Fundamental Representations and Highest
- Topics in Representation Theory: The Weyl Integral and Character Formulas
- Topics in Representation Theory: Decomposition of the Induced Representation
- Topics in Representation Theory: Borel Subgroups and Flag Manifolds
- Topics in Representation Theory: The Borel-Weil Theorem
- Topics in Representation Theory: Spin Groups 1 Spin Groups
- Topics in Representation Theory: The Metaplectic Representation
- Topics in Representation Theory: Hamiltonian Mechanics and Symplectic
- Topics in Representation Theory: The Moment Map and the Orbit Method
- Topics in Representation Theory: Other There are several other topics I hoped to have time to cover in this course
- Groups and Representations II: Syllabus Survey and History of Representation theory; Generalities about Quanti-
- Modern Geometry I: Problem Set 1 Due Monday, October 4
- Modern Geometry II: Problem Set 1 Due Monday, February 21
- Modern Geometry II: Problem Set 3 Due Monday, April 18
- Topics in Representation Theory: Cultural This semester we will be covering various topics in representation theory, see
- Groups and Representations II: Problem Set 2 Due Monday, March 3
- Groups and Representations II (Spring 2007): Survey and history of representation theory; generalities about quantiza-
- Modern Geometry II: Problem Set 2 Due Monday, March 21
- Topics in Representation Theory: Fourier Analysis and the Peter Weyl Theorem
- Topics in Representation Theory: Lie Groups, Lie Algebras and the Exponential Map
- Groups and Representations I: Problem Set 2 Due Monday, October 8
- Topics in Representation Theory: Roots and 1 The Representation Ring
- Modern Geometry This is a one-year graduate-level introduction to modern geometry, what
- Topics in Representation Theory: Roots and Complex Structures
- Modern Geometry I: Problem Set 3 Due Monday, November 8
- Groups and Representations II: Problem Set 1 Due Monday, February 5
- Groups and Representations II: Problem Set 3 Due Monday, March 31
- Topics in Representation Theory: Homogeneous Vector Bundles and Induced
- Quantum Field Theory for Mathematicians: Hamiltonian Mechanics and Symplectic
- Topics in Representation Theory: Maximal Tori and the Weyl Group
- Groups and Representations II: Problem Set 2 Due Monday, February 19
- Background on classification of Lie groups and Lie algebras
- Highest-weight Theory: Borel-Weil Math G4344, Spring 2012
- Induced Representations and Frobenius Reciprocity
- The Weyl Character Formula Math G4344, Spring 2012
- Groups and Representations, Spring 2012 Problem Set 3
- BRST and Dirac Cohomology Preliminary Draft Version
- Lie Groups and Representations, Spring 2012: Lie Groups and Lie Algebras: review of fall semester and survey of classi-
- Harmonic Analysis on Compact Lie Groups: the Peter-Weyl Theorem
- Highest-weight Theory: Verma Modules Math G4344, Spring 2012
- Groups and Representations, Spring 2012 Problem Set 2
- Lie Algebra Cohomology and the Borel-Weil-Bott Theorem
- Generalities about Representation Theory Math G4344, Spring 2012