When is a loop of string really knotted? Can one knot "cancel" another? Can you always unknot your garden hose? These are a few of the simple examples of deep questions in knot theory. The speaker will talk about these and other related questions in topology, a relatively new branch of mathematics whose ideas have penetrated nearly all areas of mathematical thought.
Abigail Thompson earned her Ph.D. from Rutgers University in 1986 and spent a few years at UC Berkeley and Hebrew University of Jerusalem before coming to UC Davis, where she is now a Professor of Mathematics. Her main research interests are in low-dimensional topology and knot theory. Last summer she was the co-director of the COSMOS program at UC Davis, a 4 week residential program for talented high school students in math and science.