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Seminar

RAS - Postdoc Seminar: On Borel Anosov representations in even dimensions & Convex co-compact representations of 3-manifold groups November 18, 2020 (09:00 AM PST - 11:00 AM PST)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Mitul Islam (University of Michigan), Kostas Tsouvalas (University of Michigan)
Description

To attend this seminar, please register here: https://www.msri.org/seminars/25205

Video

On Borel Anosov Representations In Even Dimensions

Convex Co-Compact Representations Of 3-Manifold Groups

Abstract/Media

To attend this seminar, please register here: https://www.msri.org/seminars/25205

 

Konstantinos Tsouvalas' Title and Abstract (9:00am - 9:45am):

On Borel Anosov representations in even dimensions

Anosov representations of fundamental groups of negatively curved Riemannian manifolds into reductive Lie groups were introduced by Labourie in his study of the Hitchin component. A general definition was given by Guichard-Wienhard for the class of all word hyperbolic groups. Borel Anosov representations into projective (or special) linear groups are the strongest kind of Anosov representations. In this talk, we are going to characterize which word hyperbolic groups admit Borel Anosov representations into PGL(d,R) when d is of the form 4q+2.

 

 

Mitul Islam’s Title and Abstract (10:00am-10:45am):

Convex co-compact representations of 3-manifold groups

Convex co-compact representations are a generalization of convex co-compact Kleinian groups. A discrete faithful representation into the projective linear group is called convex co-compact if its image acts co-compactly on a properly convex domain in real projective space. In this talk, I will discuss such representations of 3-manifold groups. I will prove that a closed irreducible orientable 3-manifold group admits such a representation only when the manifold is geometric (with Euclidean, Hyperbolic, or Euclidean × Hyperbolic geometry) or when each component in its geometric decomposition is hyperbolic. This extends a result of Benoist about convex real projective structures on closed 3-manifolds. In each case, I will also describe the structure of the representation and the properly convex domain. This is joint work with Andrew Zimmer. 

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On Borel Anosov Representations In Even Dimensions

H.264 Video 25524_29082_8640_On_Borel_Anosov_Representations_in_Even_Dimensions.mp4

Convex Co-Compact Representations Of 3-Manifold Groups

H.264 Video 25524_29082_8641_Convex_Co-Compact_Representations_of_3-Manifold_Groups.mp4