# Seminars

## Upcoming seminars

Title: ON IRREDUCIBLE REPRESENTATIONS OF FUCHSIAN GROUPS.

Abstract:"Let G be an almost simple simply–connected algebraic group over C. Let KG denote its maximal compact subgroup. Let R ⊂ P1 be a finite subset of distinct closed points. Recall that the fundamental group π1(P1C \ R) is a free group on s = ∥R∥-number of generators γ1,...,γs such that γ1 ...γs = 1. Recall that a subset H ⊂ KG is called irreducible if the {Y ∈ Lie(G) | adh(Y) = Y,∀h ∈ H} = centre of Lie(G) = 0 and a homomorphism ρ : π1(P1C \ R) → KG is called irreducible if the image ρ(π1(P1C \ R)) ⊂ KG is irreducible. For i ≥ 3, let {Ci|1 ≤ i ≤ s} denote a prescribed set of conjugacy classes in KG. The aim of my research is to give a verifiable criteria for the existence of an irreducible homomorphism ρ : π1(P1C \R) → KG, such that the conjugacy class of ρ(γj) lies in Cj. This research is a jointwork with Vikraman Balaji. It recently appeared online in the Canadian Journal. ".

Speaker: Yashonidhi Pandey

Date: October 09, 2024 (Wednesday)

Time: 3:30pm-4:30pm

Venue: Seminar Room 2