Stability and Testability - A Computational Perspective

Explore a comprehensive mathematical workshop examining the interconnections between stability theory, testability, and group approximations from multiple computational and algebraic perspectives. Delve into cutting-edge research presentations covering stability and testability through computational lenses, property (T) and sofic approximations for product groups, flexible stability concepts and their applications to surface groups, and the relationship between cohomology vanishing and non-approximable groups. Investigate advanced topics including Hilbert-Schmidt stability via C*-algebras, the PCP theorem's connections to locally testable codes, invariant random subgroups, and amenable group stability through ergodic theory. Examine specific group classes through presentations on Grigorchuk groups' permutation stability, crystallographic groups' matrix stability, and topological obstructions to matrix stability in discrete groups. Learn about constraint metric approximation, symplectomorphism representations via quantization, and ultrametric stability problems, while exploring why Connes' embedding conjecture was refuted and current challenges in infinite group approximations.

Syllabus

Stability and testability - a computational perspectiveJonathan Mosheiff
Stability, testability and property (T) - Oren Beker
Stability and sofic approximations for product groups and property (tau) - Adrian Ioana
Flexible stability and nonsoficity - Peter Burton
Surface groups are flexibly stable - Nir Lazarovich
Approximations of groups, subquotients of infinite direct products and equations... - Lev Glebsky
Stability, cohomology vanishing, and non-approximable groups - Andreas Thom
Vanishing of cohomology for groups acting on buildings - Izhar Oppenheim
Hilbert-Schmidt stability of groups via C*-algebras - Tatiana Shulman
The PCP theorem, locally testable codes, and property testing - Irit Dinur
Stability and Invariant Random Subgroups - Henry Bradford
Stability of amenable groups via ergodic theory - Arie Levit
Permutation stability of Grigorchuk groups - Tianyi Zheng
Non-amenable groups admitting no sofic approximation by expander graphs - Gabor Kun
Matrix stability of crystallographic groups - Soren Eilers
Norm stability in the unitary case from Voiculescu to Gromov-Lawson - Shmuel Weinberger
Topological obstructions to matrix stability of discrete groups - Marius Dadarlat
Constraint metric approximation and constraint stability - Liviu Paunescu
Approximate representations of symplectomorphisms via quantization - Leonid Polterovich
Why was Connes' embedding conjecture refuted and there are still no known... -Michael Chapman
Ultrametric stability problems - Francesco Fournier Facio
Approximations of infinite groups - Goulnara Arzhantseva