Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: Dominating PSL(n,C)-representations of punctured-surface groups
Speaker: Subhojoy Gupta, IISc
Date: March 14, 2022
Time: 16:00:00 Hours
Venue: AG-77
Abstract: For a closed and oriented surface S, Deroin-Tholozan had proved that for any representation of the fundamental group of $S$ into PSL$(2,C)$, there is a dominating Fuchsian representation. Here, domination is a notion that can be defined in terms of the marked length spectrum of the representation. They also conjectured a generalization in the context of Higgs bundles. I shall motivate and describe these, and talk of the following result for the case when S has punctures: for a generic representation of the punctured-surface group into PSL$(n,C)$, there is a dominating Hitchin representation in the same relative representation variety. The proof uses Fock-Goncharov coordinates for the moduli space of framed representations.
Title of Talk: Dominating PSL(n,C)-representations of punctured-surface groups
Speaker: Subhojoy Gupta, IISc
Date: March 14, 2022
Time: 16:00:00 Hours
Venue: AG-77
Abstract: For a closed and oriented surface S, Deroin-Tholozan had proved that for any representation of the fundamental group of $S$ into PSL$(2,C)$, there is a dominating Fuchsian representation. Here, domination is a notion that can be defined in terms of the marked length spectrum of the representation. They also conjectured a generalization in the context of Higgs bundles. I shall motivate and describe these, and talk of the following result for the case when S has punctures: for a generic representation of the punctured-surface group into PSL$(n,C)$, there is a dominating Hitchin representation in the same relative representation variety. The proof uses Fock-Goncharov coordinates for the moduli space of framed representations.