
Invited Speaker Jeff Lagarias Researcher AT&T Bell Laboratories Murray Hill, NJ 
Email: 
jcl@research.att.com 
Homepage: 
http://netlib.att.com/math/people/jcl/ 
Paper: 
The 3x+1 problem and its generalizations 
Talk: 
A new view on the Hirsch Conjecture 
Abstract: 
The Hirsch conjecture states that any ddimensional bounded polytope
with n facets has an edgepath between any two vertices of length at
most nd. The dstep conjecture is the special case n=2d, and is known
to be equivalent to the general conjecture. It has long been suspected
to be false in high dimensions. In joint work with N. Prabhu and J.
Reeds, we discovered striking evidence that it is true in all
dimensions, in a strong form. This evidence was based on a connection
with Gaussian elimination of a set of $(d!)^2$ matrices constructed
from the dpolytope with 2d facets, and massive computational
experiments.

Born: 
U.S.A 
Education: 
I got my degrees from Massachusetts Institute of Technology
(S.B./S. M. 1972 Ph.D. 1974) all in mathematics. My thesis advisor
was Harold M. Stark, with a thesis in Algebraic Number Theory.

Interests: 
I am a pretty quiet guy who enjoys reading and
going for nice leisurely runs. 
Comments: 
I'm kind of the traditional type; I am most attracted to the
permanence and stability of mathematics: I don't even own
a computer! 