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 not include a poster session.