Abstract

Modeling non-commutative phenomena in finite dimensional matrix algebras is a central theme of the program Quantitative Linear Algebra. This workshop will focus on a variety of concrete questions around this theme, coming from several directions, such as operator algebras, quantum information theory, geometric group theory, ergodic theory, etc. Topics will include: Connes approximate embedding conjecture, predicting that any II1 factor can be approximated in moments (“simulated”) by matrix algebras, with its numerous equivalent formulations in C*-algebras, quantum information, logic, etc. Related questions in combinatorial optimization, computational complexity and quantum games (e.g., the unitary matrix correlation problem). The sofic group problem, on whether any group can be “simulated” by finite permutation groups, and whether all free actions of a sofic group are sofic. Defining “good notions” of entropy for measure preserving actions of arbitrary groups (e.g., extending sofic entropy, etc). The commuting square problem for bipartite graphs, arising in subfactor theory. This workshop will include a poster session; a request for poster titles will be sent to registered participants in advance of the workshop.