Categorical dynamics: from Hopfield to Pareto

Speaker:

Matilde Marcolli

Affiliation:

Caltech

Date:

Tue, 08/03/2022 - 13:45 - 15:30

Parent event:

Algebra, Geometry and Physics: a mathematical mosaic [2]

Parent event:

Seminar on Algebra, Geometry and Physics/joint with HU Berlin [3]

This talk is part of the Algebra, Geometry and Physics Seminar [4] (MPIM/HU Berlin), host Gaetan Borot,
contact: gaetan.borot@hu-berlin.de

In recent work with Yuri Manin, we proposed a model of neural information networks based on functorial assignments of resources to networks, originating in Segal's notion of summing functors and Gamma spaces, and a corresponding categorical form of Hopfield equations on networks.
I will review some properties and examples of such categorical framework and dynamics, and I will show how it can be applied to a form of Pareto optimization.