PMATH 990
Topics in Pure Mathematics
Winter 2027 · Free and Finite Free Probability
Topics
- Free independence in noncommutative algebras
- Random Hermitian matrices and asymptotic freeness
- Additive and multiplicative free convolution
- Finite free probability
- Characteristic polynomials and polynomial convolution
Readings
- Roland Speicher, Free Probability Theory lecture notes; linked from https://www.uni-saarland.de/lehrstuhl/speicher/roland-speicher.html
- Research paper: https://arxiv.org/abs/1504.00350
- Research paper: https://arxiv.org/abs/2108.07054
Winter 2025 · Topics in Pure Mathematics - Introduction to random matrix theory
Readings
- An Introduction to Random MatricesCambridge, 2010; reference monograph.
- Random Matrices and Free ProbabilitySpringer, 2017; reference monograph.
- Todd Kemp, UC San Diego random matrix theory course notes (2022): https://mathweb.ucsd.edu/~tkemp/247A.Notes.pdf
- Roland Speicher, Saarland University random matrix course notes (2020): https://arxiv.org/abs/2009.05157
Winter 2022 · Multiprover interactive proofs with entanglement
Topics
- Entangled multiprover interactive proofs and MIP*
- Nonlocal games
- Self-testing and parallel repetition
- Proof ideas behind MIP*=RE
- Applications to operator algebras and the Connes embedding problem
Winter 2021 · Functional Analysis Methods for QIT
Topics
- Metric and topological spaces
- Banach and Hilbert spaces
- Operators on Hilbert spaces and spectral theory
- Compact operators and Schatten classes
- Unbounded operators and self-adjointness
- Stone’s theorem
- Von Neumann algebras and C*-algebras
Readings
- Instructor lecture notes are provided.
Winter 2020 · Elements of Random Matrix Theory
Readings
- An Introduction to Random MatricesCambridge, 2010.
- Random Matrices and Free ProbabilitySpringer, 2017.
- Topics in Random Matrix TheoryAmerican Mathematical Society, 2012.
Sources
- Course catalogue ↗2026–2027
- Course source ↗2023
- course_outline ↗Winter 2027
- course_outline ↗Winter 2025
- course_outline ↗Winter 2022
- course_outline ↗Winter 2021
- course_outline ↗Winter 2020
- Upcoming Winter 2027 course description; source explicitly identifies the lecture notes and two papers.
- Official public PDF outline or course description. Materials and topic extracts may be partial; consult the linked source for the full list.
- Official public PDF outline or course description. Materials and topic extracts may be partial; consult the linked source for the full list.
- Official public PDF outline or course description. Materials and topic extracts may be partial; consult the linked source for the full list.
- Official public PDF outline or course description. Materials and topic extracts may be partial; consult the linked source for the full list.