Representation theory plays a central role in many areas of mathematics, computer science and physics. In this course we build the theory of Schur-Weyl duality, highest-weight vectors, Clebsch-Gordan and Kronecker coefficients, moment polytopes, and symmetric polynomials, and then study various areas of applications including quantum information theory and quantum algorithms, optimization, and algebraic complexity theory.
Intended audience: The course is aimed at a broad audience, including mathematics students who would like to deepen their knowledge of representation theory and its (quantum) applications, or quantum computing students who would like to learn representation theory because of its many applications in quantum physics and quantum information theory / algorithms.
Prerequisites:
• Mandatory: group theory and linear algebra
• Optional: representation theory of finite groups or similar
• Optional: "Quantum Computing" or "Quantum Information Theory"
- Docent: Maris Ozols
- Docent: Jeroen Zuiddam