Operator systems and noncommutative geometryMPIM

by Malte Leimbach (MPIM)

Thursday Jun 11, 2026, 3:00 PM → 4:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

MPI-Oberseminar

Operator algebraists like to think of unital C$^*$-algebras as noncommutative compact Hausdorff spaces.
In noncommutative geometry, additional metric space structure is provided by a noncommutative version of the optimal transport cost.
This concept of distance still makes sense when relaxing the C$^*$-algebraic setting, as long as there is enough algebraic structure to make sense of states (= noncommutative probability measures):
the structure in question is called an \emph{operator system}.
    Operator systems are easy to define, but allow for a rich theory, contributing to the interplay between operator algebras and quantum information theory.
Moreover, they are suitable for incorporating spectral truncations and constrained spatial resolution in noncommutative geometry.
This talk will point out some of the highlights of the theory of operator systems and of the recent approach to noncommutative geometry in terms of operator systems, with emphasis on the metric aspect.