This seminar series is co-presented by SMRI. Algebra seminars (2022-) and former SMRI Algebra and Geometry Online (SAGO) seminars are specialised research talks by international researchers in algebra and geometry.
Algebra Seminar ‘On the Real Spectrum Compactification of Character Varieties’
Marc Burger, ETH Zürich
Friday 10 March 2023
Abstract: For a finitely generated group F and a real algebraic semisimple group G, the set of conjugacy classes of G-representations of F is naturally a real semi algebraic set, called the G-character “variety” of F. For instance when F is the fundamental group of a closed surface then, depending on G, certain connected components of the G-character variety of F consist entirely of injective representations with discrete image: these are the so called “higher Teichmueller spaces”. The real spectrum of areal algebraic set provides then a compactification of all its semialgebraic subsets and leads to interesting compactifications of higher Teichmueller spaces. I will describe some of the properties of these compactifications and relate them to other known compactifications. This is part of an ongoing project with Alessandra Iozzi, Anne Parreau and Beatrice Pozzetti.