Abstract
Mathematicians classify abstract objects, similar to how other scientists classify biological species, chemical elements, or stars.
A classification can be discrete (and even finite), or it can be continuous. In the latter case, it is described using a moduli space. This is book-keeping device used by a mathematician, and it is itself a geometric object. Different points in the moduli space correspond to different objects that are being classified, in such a way that slightly perturbing the point in the space corresponds to slightly perturbing the classified object.
I will survey the mathematician’s urge to classify objects, and how moduli spaces provide the perfect toolkit for this purpose. I will end with some examples from my own research.
Programme
17.30 Introduction
17.35 Lecture by Prof. Pieter Belmans
18.15 Questions and Answers
18.30 Cocktail
Biography
Prof. Dr. Pieter Belmans started at the University of Luxembourg in August 2021, building up a research group on algebraic geometry, noncommutative algebra, and representation theory. Before joining the University of Luxembourg, he was a postdoc at the Universities of Bonn and Antwerp, and the Max Planck Institute in Bonn. His research focuses on understanding the similarities and differences between certain families of moduli spaces, and on noncommutative algebraic geometry. His work often features a computational component, in a usually highly abstract field. He is also very active in making mathematics accessible online, and creating interactive classification websites.