Non-commutative Optimal Transport - Spring 2025 - IPAM at UCLA

Описание: Apply to attend: https://www.ipam.ucla.edu/programs/lo...

"Non-commutative Optimal Transport" is the Spring 2025 long program at the Institute for Pure and Applied Mathematics at UCLA. In this webinar, Selenne Bañuelos, the Associate Director of IPAM, explains the resources provided to long program participants and then Augusto Gerolin of the University of Ottawa goes into detail about the themes of the three main week-long workshops.

Overview:
In the last decades, optimal transportation (OT) has emerged as a fertile field of inquiry, and an effective tool for the diverse exploration of applications within and beyond mathematics, including economics, meteorology, geometry, statistics, fluid mechanics, engineering, and design problems.
More recently, motivated by fundamental problems in Artificial Intelligence, Quantum Physics, and Electronic Structure Theory, the theory of OT has been broadening to a different class of state spaces such as the spaces of density matrices, operators, or more generally C* and von Neumann algebras, all of which are non-commutative. Although these non-commutative OT variants share a common mathematical feature, a unified geometrical perspective for them is still lacking. Additionally, many crucial analytical, computational, and statistical challenges remain unsolved, impeding the development of practical applications.
The program brings together and fosters collaborations among researchers from complementing mathematical communities that have been or are keen on working on the topic. More specifically, the program will focus on:
Evolution equations for density operators
Quantum optimal transport
Wasserstein distances for density operators
Semidefinite relaxation of non-commutative transport
Statistical and probabilistic aspects of non-commutative transport
Matrix and Operator Functional inequalities
Computational algorithms solving non-commutative optimal transport

Apply to attend: https://www.ipam.ucla.edu/programs/lo...