• Speaker: Brent Nelson, MSU
• Title: Making Weight
• Date: 09/12/2022
• Time: 4:00 PM - 5:30 PM
• Place: C517 Wells Hall
• Contact: Brent Nelson (banelson@msu.edu)

A weight on a von Neumann algebra is a positive linear map that is permitted to be infinitely valued. It is a generalization of a positive linear functional that arises naturally in the context of crossed products by non-discrete groups, and they are vital to the study of purely infinite von Neumann algebras. In this talk I will provide an introduction to the theory of weights that assumes only the definition of a von Neumann algebra.

• Speaker: Aldo Garcia Guinto, MSU
• Title: Conjugate Variables and Dual Systems
• Date: 09/26/2022
• Time: 4:00 PM - 5:30 PM
• Place: C517 Wells Hall
• Contact: Brent Nelson (banelson@msu.edu)

In free probability, the semi-circular operators are the analogue of the Gaussian distribution in classical probability. We will be using the semi-circular operators to motivate two notions of free probability: conjugate variables and dual systems. The conjugate variables are used to define free Fisher information, which is analogue of Fisher information in classical probability. While the dual systems are related to a cohomology theory for von Neumann algebras. It turns out that these two notions are not as different as they may seem.