Seminar: Berkan Üze - Categorical themes in information theory (Feb 20, 2026)

Categorical themes in information theory
Berkan Üze

While tantalizingly titled, this informal talk is merely intended to motivate some recent avenues of research on algebraic and categorical structures implicit in information and probability theory. We will give a brief thematic overview, starting with the seminal result that Shannon entropy can be characterized by a certain universal property as the unique function satisfying a functional equation that has come to be called the fundamental equation of information theory. A collection of results and observations by Kontsevich, Elbaz-Vincent, Gangl and others have furthered this theme in a direction which involves a rich interplay of fundamental concepts in arithmetic geometry and theory of polylogarithms. After a brief discussion of these results, we will introduce the theory of information cohomology due to Baudot and Bennequin which is expected to formalize some of these insights.