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Seminar

RAS - Research Seminar (Part 1): Non-left orderability of lattices in higher rank Lie groups September 21, 2020 (09:00 AM PDT - 10:00 AM PDT)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Sebastian Hurtado Salazar (University of Chicago)
Description

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

This is one of the research seminars for the RAS program, that distinguishes itself from the postdocs and program associates seminars in that speakers are chosen among Research Members, Research Professors with occasional outside speakers.

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Abstract/Media

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

(Joint work with Bertrand Deroin).

Abstract:

A countable group is said to be  left-orderable if it preserves a total order invariant by left multiplication or equivalently if it embeds in the group of homeomorphisms of the line. I'll explain the basics of left orderability, a new perspective in the study of left orderable groups and what is known about left orderability of lattices in Lie groups.

Our main result is that a lattice in a real semi-simple Lie group G of higher rank is left orderable if and only if G is a product of two Lie groups and one factor is the universal covering of SL_2(R). In particular, every lattice in SL_n(R) (if n > 2) is not left orderable. This solves conjectures of Witte-Morris and Ghys.

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