[Binghamton Geometry/Topology Seminar] Geometry & Topology seminar

[somnath at math.binghamton.edu]

BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR

*Date:*  Thursday, April 4, 2013

*Time:*  2:50-3:50pm
*Place:*  Library North 2205 followed by coffee/tea in the Anderson Reading
Room.

*Speaker: ** *Andrew Sale (Cornell University)
*Title: *A Geometric Version of the Conjugacy Problem in Semisimple Lie
Groups
 *
Abstract:* For a finitely generated group, the conjugacy problem asks if
there is an algorithm which determines whether a pair of elements are
conjugate or not. This is one of Max Dehn's well-known decision problems
and has been widely studied over the past century. Related to this problem
is the question of understanding, for a pair of conjugate elements, the
family of conjugators between them. We focus in particular on estimating
the minimal length of such an element. This problem naturally extends
beyond the reach of the conjugacy problem itself and can be asked of any
group which admits a left-invariant metric. We will discuss a result for
pairs of hyperbolic elements in a semisimple Lie group. The issue of
extending results from here to their lattices, such as SL(n,Z), remains
unsolved, with questions raised of a number theoretic nature.