This week, Dave Futer is giving two introductory talks on knot theory to undergraduate audiences.
Talk #2 will take place Thursday, October 27, at 4:30 PM here at Temple, in 617 Wachman Hall.
Title: The space around a knot
Abstract: On the wall in my parents’ garage hangs a tangled extension cord with one end plugged into the other. I have tried to untangle it, without separating the two ends and breaking the circle – and had no success. Does this mean I haven’t tried the right strategy, or is it theoretically impossible? Is there a procedure that can tell if an extension cord is truly knotted, or if two different cords contain the same knot?
This kind of study of knotted circles began in the 19th century with some odd notions about atoms. Since then, it blossomed into a beautiful geometric discipline whose problems have applications to both biology and physics. I will describe a way to study and compare knots by understanding the space that surrounds a knot.