GROW 2015 Talk Titles and Abstracts
Abstract: Lord Kelvin proposed that knots were the elements of nature, and with his proposal the mathematical quest to classify knots was born. I will briefly review a piece of this theory, then describe some counterparts for Legendrian knots, which obey a particular differential equation. Everything can be described with simple pictures drawn in the plane. Yet despite the basic setting, these knot constructions offer access to some deeper mathematical structures such as quivers, flag varieties, and categories.
Abstract: Take a natural number n, and look at all possible ways to break up the numbers from 1 to n into several groups. These are called partitions. Two partitions are linked if one can be obtained from the other by breaking up some groups. Three partitions are linked if one is obtained from the other by breaking up, and the third is obtained by breaking up further. Similarly we can define when any number of partitions are linked. Studying these linkage properties gives rise to a shape associated to the number n, whose symmetries know about deep structures in algebraic topology.Sunday, 25 October, 0930-1015
Abstract: Lay 6 sticks on the ground and attach them end-to-end to form a polygon. What angles do they form? How flexible is your polygon? Try this with 7 sticks or 8, or keep your 6 sticks but change their lengths; now what angles can they form? It turns out that there is no simple way to compute these angles -- or at least no one knows the answer. I will talk about this question and how it relates to other questions in geometry, algebra, dynamical systems, and computational mathematics.Back to top