Colloqiuim- Coloring knot diagrams and quandles

Title: Coloring knot diagrams and quandles

Speaker:  Masahiko Saito, Univ. of South Florida

Date and Time: Friday, February 22, 2:00-3:00pm

Place: Rome 206

Abstract :  A knot is a circle embedded in 3-space. A main problem in knot theory is to distinguish them up to continuous deformation. A typical method is to find assignments of algebraic objects called  knot invariants, such as numbers, to knot diagrams. Coloring knot diagrams have been used to construct knot invariants. After a brief overview of basic methods in knot theory, we introduce a self-distributive algebraic structure called quandles, that is used to color knot diagrams. We then assign weights at crossings of knot diagrams colored by quandles, to obtain stronger invariants.This is based on an algebraic homology theory for quandles, which is briefly explained. We will also discuss how to generalize this method to the next dimension, knotted surfaces in 4-space.

Bio: Masahico Saito is a Professor of Mathematics at the University of South Florida. After graduating with Ph.D. from University of Texas at Austin, he held visiting positions at University of Toronto and Northwestern University. His research focuses on knot theory, related algebraic structures, and applications of discrete and topological methods to DNA assembly.