Research Seminars @ Illinois

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Tailored for undergraduate researchers, this calendar is a curated list of research seminars at the University of Illinois. Explore the diverse world of research and expand your knowledge through engaging sessions designed to inspire and enlighten.

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GGT seminar: Bending deformations and the arithmetic of surface group representations

Event Type: Seminar/Symposium
Sponsor: Groups, Geometry, and Topology Seminar
Location: 347 Altgeld Hall
Date: Feb 27, 2025 11:00 am - 12:00 pm
Speaker: Michael Zshornack (Northwestern)
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Originating Calendar: Groups, Geometry, and Topology Calendar; "Bending" is a fairly elementary construction that allows one to produce new representations of surface groups from old ones. The geometry associated to these deformations has been studied by many, for instance, Thurston, in constructing examples of quasi-Fuchsian groups. Recently, the utility of these deformations in more arithmetic contexts has come to light following several results using bending to produce thin surface subgroups in many higher-rank lattices. I'll explain what these deformations are and their applications to understanding arithmetic properties of higher-rank Teichmüller spaces. Time permitting, I'll also discuss some applications towards representation varieties of surface groups into p-adic groups. This is based, in part, on joint work with Jacques Audibert.

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