The GT seminar meets on Fridays at 2:00pm Fridays in room 520. We also have an overflow room 622 from 11 to 1 Fridays for additional talks.
Organizer: Walter Neumann.
Other area seminars. Our e-mail list. Archive of previous semesters
|TBA||Tarik Aougab, Brown|
|Jan 25||Khalid Bou-Rabee, CUNY||On local residual finiteness of abstract commensurators of Fuchsian groups|
|Mar 29||Ronno Das, Chicago|
|Apr 12||Oishee Banerjee, Chicago|
|Apr 26||Daryl Cooper, UCSB|
Tarik Aougab, Brown
Khalid Bou-Rabee, CUNY
January 25, 2019,
Title: On local residual finiteness of abstract commensurators of Fuchsian groups
Abstract: The abstract commensurator (aka ``virtual automorphisms'') of a group encodes ``hidden symmetries'', and is a natural generalization of the automorphism group. In this talk, I will give an introduction to these mysterious and classical groups and then discuss their residual finiteness. Recall that residual finiteness is a property enjoyed by linear groups (by A. I. Malcev), mapping class groups of closed oriented surfaces (by EK Grossman), and branch groups (by definition!). Moreover, by work of Armand Borel, Gregory Margulis, G. D. Mostow, and Gopal Prasad, the abstract commensurator of any irreducible lattice in any ``nice enough'' semisimple Lie group is locally residually finite (a property is termed ``local'' if it is satisfied by every finitely generated subgroup of the group). ``Nice enough'' is sufficiently broad that the only remaining unknown case is PSL_2(R). Are abstract commensurators of lattices in PSL_2(R) locally residually finite? Lattices here are commensurable with either a free group of rank 2 or the fundamental group of an oriented surface of genus 2. I will present a complete answer to this decades old question with a proof that is computer-assisted. Our answer and methods open up new questions and research directions, so graduate students are especially encouraged to attend. This talk covers joint work with Daniel Studenmund.
Ronno Das, Chicago
Oishee Banerjee, Chicago
Daryl Cooper, UCSB
Other relevant information.Fall 2018, Spring 2018, Fall 2017, Spring 2017, Fall 2016, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, 2010/11, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007, Spring 2007, Fall 2006.
- Columbia Symplectic Geometry/Gauge Theory Seminar
- All Columbia Math Dept Seminars
- CUNY Geometry and Topology Seminar
- CUNY Complex Analysis & Dynamics Seminar
- CUNY Magnus Seminar
- Princeton Topology Seminar.