Graduate Student

Event Information Platonic solids and the McKay correspondence
17:45 on Thursday November 05, 2015
18:45 on Thursday November 05, 2015
BA6180, Bahen Center, 40 St. George St.
Louis-Philippe Thibault
https://www.math.toronto.edu/cms/thibault-louis-philippe/
University of Toronto

Through the theory of resolution of singularities, Du Val discovered in 1934 a correspondence between finite subgroups of $SL(2, \mathbb C)$ and extended simply-laced Coxeter-Dynkin diagrams, which appear in many different contexts in Mathematics. In 1979, McKay observed that this correspondence could be established directly by looking at the structure of the groups and their representations. This allowed a whole new understanding of the geometry and algebra of singularities and their resolution and have given rise to many beautiful results. In this talk, we will first describe the classification of finite subgroups of $SL(2, \mathbb C)$, which was done trough the work of Hessel, Klein and Hamilton in the 19th century and involves Platonic solids. We will then give some intuition about resolution of singularities and Du Val’s result. Finally, we will explain basic representation theory of finite groups and establish the McKay correspondence.

Reminder: pizza will be provided at the seminar (at 5:30PM) and there will be a pub-night afterwards, subsidized by the MGSA.