Speaker: Vyron Vellis, UTK
Title: Analysis on thin Cantor sets
Abstract: A set X is called uniformly disconnected (thin) if for any x in X and any r>0 there exists an isolated island E in X that contains x, has diameter at most r and distance from X-E at least a fixed multiple of r. First, we give a geometrical uniformization result for all thin Cantor sets that generalizes a result of MacManus from 2 to all dimensions. Then we give three applications of this theorem; the first in complex dynamics (Julia sets of UQR maps), the second in hyperbolic geometry (pants decompositions of Riemann surfaces of infinite type), and the third in geometric function theory (Decomposition Problem for planar bi-Lipschitz mappings). The talk is based on works partially joint with Alastair Fletcher.
Friday, September 17 at 3:35pm to 4:35pm
Ayres Hall, 405
1403 Circle Drive, Knoxville, TN 37996