Abstract: 

Abstract: A Kirby diagram presents a handle decomposition on a 4-manifold as a framed link in connected sums of S¹xS². I will introduce Kirby calculus, a successful approach to studying 4-dimensional manifolds, and a geometric structure called an open book. This talk aims to provide an algorithm for constructing a Kirby diagram of a 4-dimensional open book and discuss its applications.

Abstract: A contact 3-manifold is a smooth 3-manifold equipped with an extra geometric structure. Knots in contact 3-manifolds are interesting objects to study. There are two types of knots in a  

contact manifold - Legendrian and transverse. In this talk, I will give a gentle introduction to contact manifolds and Legendrian knots. I'll discuss some of their applications and why one would study them.

No background knowledge of contact topology will be assumed.

Abstract: In my talk, I will cover different applications to entangled materials and overall applications related to knot theory. My personal interest lies in Topological Data Analysis and how it can be applied to both real-world data and more mathematically rigorous structures. I will focus on the silk-worm cocoon as an example of a complex microstructure, producing a complicated entangled material. We approach this data through the lens of persistent homology to derive conclusions about pore size gradients and fiber thickness gradients. Analyzing the fiber alignments we demonstrate the uniform fiber orientations.