[Binghamton Geometry/Topology Seminar] Binghamton Geometry-Topology seminar

[Ross Geoghegan]

  BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR


    Date: Thursday, September 11, 2014

    Time:  2.50 pm

    Place: Old Whitney Hall, Room 100E,  followed by coffee/tea in the Hilton
           Reading Room. Note the new location of the math department


    Speaker: Ben McReynolds (Purdue University)

    Title: Effective rigidity and counting

Abstract:

In 1992, Alan Reid proved that if two arithmetic hyperbolic 2-manifolds
have the same geodesic length spectrum, the two manifolds must be
commensurable. In 2008, Chinburg-Hamilton-Long-Reid extended Reid's
result to arithmetic hyperbolic 3-manifolds. In this talk, I will
discuss effective versions of these results. Specifically, given two
arithmetic hyperbolic 2- or 3-manifolds of some bounded volume V that
are not commensurable, we ensure that a length L occurs in one but not
both. More important, the length L can be bounded above as a function of
the volume V and is explicitly given. These results rely on effective
rigidity results for quaternion algebras. The main tools used are
algebraic and geometric counting results of independent interest. Time
permitting, I will discuss some of these counting results. This work is
joint with Benjamin Linowitz, Paul Pollack, and Lola Thompson.

NOTE:  The seminar has a webpage where the semester's program is listed:

http://www2.math.binghamton.edu/p/seminars/topsem

It can also be linked from the Department's Home Page.