Seminar on Category Theory and its Applications

Organizer: Simona Paoli


Category Theory 

Category theory is an overarching area of mathematics studying the underlying common language describing structures arising in different contexts. This approach provides powerful tools for applications.

The area witnessed an explosion of interest in recent years and led to the discovery of new connections and synergies between areas of science.  For example, while it has been well known that the same category theoretic structures are underlying both geometry and logic, this close relationship is currently extended to higher categories and is giving rise to the area of homotopy type theory, which draws both algebraic topology and the theory of proof assistants developed in dependent type theory.

In computer science, these developments are important in the study of the semantics of programming languages, in logic in computers science and in verification. In particular, there are novel fascinating connection to so-called nominal calculi which underpin areas such as distributed systems and cloud computing.

In mathematics, higher categories have been reshaping the foundations of algebraic topology, where the classical fundamental objects of study (the topological spaces) were replaced by new and more complex structures (the infinity categories) encoding information on the higher algebraic invariants of spaces. This approach lead to important applications to homotopy theory and algebraic geometry.

In mathematical physics higher categorical structures led, among others, to the description of the mathematics underlying quantum gravity, and to the proof of long standing conjectures such as the cobordism hypothesis.

Aim of the seminar

The seminar aims to provide a platform for discussion of category theory both in its foundational aspects and in applications to computer science, logic and semantics, homotopy theory, algebraic geometry, mathematical physics. We are also interested in exploring possible applications of category theory to economics and the social sciences.

Style and timing of the talks

We welcome both expository talks and talks about recent results. We encourage to present in a way that is as accessible as possible to a diverse audience as well as to PhD students. The latter are particularly encouraged to present. The style of the seminar is informal, questions and interaction with the audience are encouraged. 

The seminar runs throughout the calendar year. We are open to use technology (webinar, skype etc) to make the seminar accessible if you are not on campus.

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