Thursday, 8 January 1998, 4:00 pm
Mathematics Bldg., lecture hall 2
Prof. Jim Cannon (Brigham Young University)
"The complex dynamics of planar subdivision rules."
Abstract:
A large triangle can quickly be cut into small triangles
by barycentric subdivision; this subdivision process, carried out
an arbitrary finite number of times, is central in geometry and
topology (homology and cohomology theory, simplicial complexes,
classification of manifolds, etc.).
We study more general subdivision rules arising in the differential
geometric study of 3-manifolds. We are led to ask, "What happens
asymptotically when a subdivision rule is applied infinitely often?
Are there intrinsic geometric stresses and strains in the rule? Is
one naturally approximating some intrinsic geometry associated
with the rule? Is the intrinsic geometry Euclidean or non-Euclidean?
Do the tiles admit optimal geometric shapes? Are the intrinsic
optimal shapes smooth? analytic? fractal? With shapes optimized,
is subdivision geometric? Conformal?
We shall indicate why a major part of Thurston's hyperbolization
conjecture for negatively curved 3-manifolds is equivalent to such
a question.
Please come for Coffee, cookies, and Company
at 3:45 pm in room 12 of the mathematics building.
Please come
to the "after colloquium coffee chat" in Beit-Belgia.
