Jerusalem Mathematics Colloquium

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.

List of talks, fall 1997