Srivatsav K Elayavalli
University of California, Los Angeles, USA
August 10, 2023
New horizons in non-commutative Voiculescu entropy: I will motivate and describe the theory of Voiculescu's free entropy in the setting of tracial von Neumann algebras which are a non commutative generalization of measure spaces. I will then describe a modern advance due to K. Jung that opened up a new dynamical perspective pushed in the works of B. Hayes, that has led to the recent resolution of the Peterson-Thom conjecture which yields the strongest rigidity results known till date of the von Neumann algebras associated to the free groups. I will describe recent works of mine with collaborators resolving a well known open question on the structure of the ultrapowers of the free group von Neumann algebras. The proof of this result uses a delicate combination of entropy techniques with Popa's deformation rigidity theory.
University of California, Los Angeles, USA
August 10, 2023
New horizons in non-commutative Voiculescu entropy: I will motivate and describe the theory of Voiculescu's free entropy in the setting of tracial von Neumann algebras which are a non commutative generalization of measure spaces. I will then describe a modern advance due to K. Jung that opened up a new dynamical perspective pushed in the works of B. Hayes, that has led to the recent resolution of the Peterson-Thom conjecture which yields the strongest rigidity results known till date of the von Neumann algebras associated to the free groups. I will describe recent works of mine with collaborators resolving a well known open question on the structure of the ultrapowers of the free group von Neumann algebras. The proof of this result uses a delicate combination of entropy techniques with Popa's deformation rigidity theory.