Explore the intersection of free probability theory and random matrix theory through this comprehensive workshop featuring expert lectures and research presentations. Delve into Voiculescu's groundbreaking work from the 1980s that connected free group factors in von Neumann algebras with the large N-limits of independent random matrices, establishing the foundation for free probability as an interdisciplinary field. Examine recent spectacular advances including the resolution of the Peterson–Thom conjecture through Hayes's 1-bounded entropy methods, which has opened new pathways in operator algebra research. Study key topics including free entropy dimension and 1-bounded entropy theory, strong and weak convergence of laws in random matrix theory, applications to von Neumann algebras and random graphs, and the far-reaching consequences of solving the Peterson–Thom Conjecture. Learn from leading researchers as they present cutting-edge work on spectral large deviations of sparse random matrices, multiplicative Brownian motions, matrix concentration theory, precise eigenvalue location for random regular graphs, the Airy-beta line ensemble, Horn's problem in free probability, and operator norm estimates for tensor-valued random matrices. Gain insights into advanced mathematical concepts through detailed minicourses on strong convergence theory and 1-bounded entropy, while exploring connections between harmonic analysis, probability theory, combinatorics, and operator algebras that make free probability such a rich and versatile mathematical framework.

Syllabus

Yoonkyeong Lee - On conjugate systems with respect to completely positive maps - IPAM at UCLA
Ella Hiesmayr - Spectral large deviations of sparse random matrices - IPAM at UCLA
Jennifer Pi - A Classical Approach for Relating Free Entropic Quantities - IPAM at UCLA
March Boedihardjo - Injective norm of random tensors - IPAM at UCLA
Chi-Fang Chen - A new approach to 1/N expansion in random matrix theory - IPAM at UCLA
Hui Tan - Some applications of Shlyakhtenko’s M-valued semicircular systems - IPAM at UCLA
Marwa Banna - Strong Convergence for Multiplicative Brownian Motions on the General Linear Group
Ramon van Handel - Strong convergence I - Minicourse, Pt. 1 of 2 - IPAM at UCLA
Tatiana Brailovskaya - Matrix concentration and strong convergence - IPAM at UCLA
Dan-Virgil Voiculescu - Around Free Entropy - IPAM at UCLA
Ramon van Handel - Strong convergence II - Minicourse, Pt. 2 of 2 - IPAM at UCLA
Jorge Garza Vargas - A new approach to strong convergence - IPAM at UCLA
Theo McKenzie - Precise Eigenvalue Location for Random Regular Graphs - IPAM at UCLA
Hariharan Narayanan - On the randomized Horn problem and the surface tension of hives - IPAM at UCLA
Jesse Peterson - A hierarchy of Haagerup-type approximation properties - IPAM at UCLA
Vadim Gorin - The Airy-beta line ensemble - IPAM at UCLA
Samuel Johnston - Horn's problem and free probability - IPAM at UCLA
Benoit Collins - Operator norm estimates for sums of tensor-valued random Haar unitaries
Ben Hayes - Invitation to 1-bounded entropy theory- Minicourse, Pt. 1 of 2 - IPAM at UCLA
Félix Parraud - The spectrum of tensor of random and deterministic matrices - IPAM at UCLA
David Gao - Sofic actions on sets and graphs - IPAM at UCLA
Ping Zhong - Limiting Eigenvalue Distribution and Outliers of Deformed Single Ring Random Matrices
Octavio Arizmendi - Limit Theorems in Finite Free Probability - IPAM at UCLA
Ben Hayes - Invitation to 1-bounded entropy theory- Minicourse, Pt. 2 of 2 - IPAM at UCLA
Aldo Garcia Guinto - Schreier's Formula for some Free Probability Invariants - IPAM at UCLA