• Lecturer: Paolo Perrone
• Date: Wednesday 11:00 - 12:30
• Room: MPI MiS, A3 02
• Language: English
• Target audience: MSc students, PhD students, Postdocs
• Keywords: Categories, functors, universal properties, applications
• Prerequisites: Basic mathematical knowledge (linear algebra, basic analysis)
• Remarks: Participants can give a lecture too (if they want).

Abstract

This course is meant as an introduction to the concepts and methods of category theory from a rather applied point of view. We will review the basic ideas, such as:

• Categories, functors, natural transformations. What it means for a construction to be "functorial", or "natural", and why it is important;
• The Yoneda lemma, a.k.a. how objects are determined purely by the way they interact with one another. How to reason in terms of diagrams, and what why it is helpful;
• Universal properties, limits, colimits, why they are everywhere, and how they generalize constrained optimization.

Category theory has been central to the development of fields such as algebraic topology, algebraic geometry, and group theory. It has also many applications to general topology, analysis, and geometry. Recently, it has been applied to some subjects of more "applied" flavor, such as:

• Networks and complexity;
• Graphical models and statistical inference;
• Data structures and classes in computer science;
• ...and many more.

Depending on the interests of the participants, we will choose one or two of these particular applications to study in detail.