Short course on Nonabelian Hodge theory
by Prof. Florent Schaffhauser (Universidad de Los Andes; Max Planck Institute Bonn; University of Strasbourg)
Prof. Florent Schaffhauser gave a series of 7 lectures on the Nonabelian Hodge Correspondence. This is an important topic of current research which spans differential geometry, analysis, physics and also algebraic geometry. It originated from four-dimensional Yang-Mills theory in the 1980s, when N. Hitchin started to investigate the two-dimensional reduction of the Yang-Mills equations, and introduced the concept of Higgs field and what became known later as the Hitchin equations.
It is difficult for students to enter this area, as significant background knowledge is required from several different fields, and there is no standard textbook. Prof. Schaffhauser gave a careful introduction to this theory, with proofs, and ideas behind proofs, wherever possible. He also gave very informative comments on the history and motivation for the subject. These aspects were greatly appreciated by the audience of around 20 participants.
After each lecture (excluding the first and last), a discussion session was held, in order to provide time for additional questions and discussions. At these sessions, short presentations on related topics were given by PhD students – 3 from Waseda and 1 each from Germany and France. These sessions contributed further to an enjoyable and instructive event.