Workshop II: Approximation Properties in Operator Algebras and Ergodic Theory

Part of the Long Program Quantitative Linear Algebra
April 30 - May 5, 2018


QLA Image #2Modeling 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.

Organizing Committee

Tim Austin (University of California, Los Angeles (UCLA))
Assaf Naor (Princeton University)
Gilles Pisier (Texas A&M University - College Station)
Sorin Popa (University of California, Los Angeles (UCLA))
Stefaan Vaes (KU Leuven )