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  Scientific Committee:
Gilbert Baumslag ,The City College of NY
Rostislav Grigorchuk,Texas A&M
Alexei Miasnikov, Stevens Institute
Mark Sapir, Vanderbilt

 

   Organizing Committee:
Murray Elder, Univ. of Newcastle (Aus)
Bob Gilman, Stevens Institute
Alexei Miasnikov , Stevens Institute
Alex Myasnikov, Stevens Institute
Denis Serbin, Stevens Institute
Alexander Ushakov, Stevens Institute

 

   Contact Information:
Denis Serbin
email:   dserbin stevens.edu    
phone: (201) 216-5425

 

   Our sponsors:

 

 

Welcome to the First Online Seminar dedicated to Group Theory and Non-Commutative Algebra.

The seminar presents a unique opportunity for mathematicians from around the world to communicate and share their ideas on a regular basis without leaving the office or even home. Participants include faculty and students from US, Canada, Australia, Europe and Russia.

If you are a first-time participant please visit the technical advice page.

Click here to enter the meeting room


Next Presentation
   Thursday,  May 5,  noon  (New York Time)

Oleg Bogopolski
(Heinrich-Heine-Universität Düsseldorf, Germany)


"From local to global conjugacy in relatively hyperbolic groups"

Click here to enter the meeting room

Abstract:
Relatively hyperbolic groups were introduced by Gromov (1987). It is known (see Hrushka (2010)) that essentially different definitions given by Gromov, Bowditch, and Osin coincide in the case, where the ambient group is countable and the peripheral subgroups are infinite. In the first part of my talk I will recall the combinatorial definition of Osin and formulate some statements which help to work in this area. In the second part I will explain new results concerning the conjugacy of subgroups in relatively hyperbolic groups. In particular, we prove the following theorem.

Theorem. Suppose that a finitely generated group G is hyperbolic relative to a collection of subgroups P. Let H1, H2 be subgroups of G such that H1 is relatively quasiconvex with respect to P and H2 has a loxodromic element. Suppose that H2 is element-wise conjugate into H1. Then there exists a finite index subgroup of H2 which is conjugate into H1. The minimal length of the conjugator can be estimated.

Corollary. Let G be a limit group and let H1 and H2 be subgroups of G, where H1 is finitely generated. Suppose that H2 is element-wise conjugate into H1. Then there exists a finite index subgroup of H2 which is conjugate into H1.

The index depends only on H1. The minimal length of the conjugator can be estimated. This implies that limit groups are subgroup conjugacy separable.
Other theorems concerning hyperbolic virtually compact special groups will be given in the talk.
This is a joint work with K.-U. Bux.

Seminar Schedule Spring 2016
Mar  17   Artem Dudko (Stony Brook University)
"On spectra and spectral measures of Koopman, groupoid and quasi-regular representations"
Abstract      PDF Slides      Watch the recording ...
 
Mar  31   Ashot Minasyan (University of Southampton, UK)
"Conjugacy separability of non-positively curved groups"
Abstract      PDF Slides      Watch the recording ...
 
Apr  14   Enric Ventura (Universitat Politecnica de Catalunya, Spain)
"Fixed subgroups are compressed in surface groups"
Abstract      PDF Slides      Watch the recording ...
 
May   5   Oleg Bogopolski (Heinrich-Heine-Universität Düsseldorf, Germany)
"From local to global conjugacy in relatively hyperbolic groups"
Abstract     
 
May  12   Shane O'Rourke (Cork Institute of Technology, Ireland)
"A combination theorem for affine tree-free groups"
   

For information on the website or other questions please contact
Alex Myasnikov: amyasnik@stevens.edu
(201) 216-8598
Stevens Institute of Technology
Hoboken, NJ