Binghamton University


MATHEMATICAL SCIENCES
COLLOQUIUM


DATE: Thursday, April 14, 2005
TIME: 4:30 - 5:30 PM
PLACE: LN 2205
SPEAKER: Jack Graver (Syracuse)
TITLE: When Does a Curve Bound a Distorted Disk?

Abstract


Consider a closed curve in the plane that does not intersect itself; by the Jordan Curve Theorem, it bounds a distorted disk. Now consider a closed curve that intersects itself, perhaps several times. Is it the boundary of a distorted disk that overlaps itself? If it is, is that distorted disk essentially unique? The question of when an immersion of the circle can be extended to an immersion of a disk has been studied by several people, notably Titus [C. J. Titus, The combinatorial topology of analytic functions on the boundary of a disk, Acta Math. 106 (1961), 45-64.] and Blank [S. J. Blank, Extending immersions of the circle, Dissertation, Brandeis University, Mass. (1967)]. I will discuss their work and then I will develop combinatorial techniques for answering these questions.

R E F R E S H M E N T S

4:00 To 4:25 PM
Kenneth W. Anderson
Memorial Reading Room