Graduate Student Colloquium
Andrew Brasile
UIC
Boundary Slopes of Knot Complements
Abstract: The set of boundary slopes of essential surfaces of a knot complement has been
the object of study for several decades. It is an important invariant of the knot and has
applications to Dehn fillings and the Neuwirth Conjecture. Studying this set makes use
of theory from a surprising variety of fields including complex analysis, tropical geometry,
linear algebra and group theory. We will establish these applications and connections to
other fields and finally discuss an approach for finding the set of boundary slopes of essential
surfaces of knot complements.
This talk is intended to be accessible for graduate students of all levels; no technical knowledge of knot theory is expected.
Monday April 9, 2012 at 4:15 PM in SEO 636