Juan Pablo Vigneaux: "Cohomological aspects of information"

Topos Institute Colloquium, 25th of January 2024.
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This talk will discuss the cohomological aspects of information functions within the framework of information cohomology (first introduced by Baudot and Bennequin in 2015). Several known functionals can be identified as cohomology classes in this framework, including the Shannon entropy of discrete probability measures and the differential entropy and underlying dimension of continuous measures. I’ll try to provide an accessible overview of the foundations of the theory, which should require only a basic familiarity with category theory and homological algebra, and survey the main known results. Finally, I'll discuss some perspectives and open problems: firstly in connection with Renyi's information dimension and other (possibly geometric) invariants of laws taking values on manifolds, and secondly with notions of entropy for categories (akin to Leinster's diversity of metric spaces).