TBD
12-4-24
4:30-5:20
Speaker: Megan Fairchild (LSU)
Abstract: Whitehead doubles provide a plethora of examples of knots that are topologically slice but not smoothly slice. We discuss the problem of the Whitehead double of the Figure 8 knot and survey commonly used techniques to obstructing sliceness. Additionally, we improve bounds in general for the non-orientable 4 genus of t-twisted Whitehead doubles and provide genus 1 non-orientable cobordisms to cable knots.
11-6-24
4:30-5:20
Speaker: Jesse Osnes
Abstract: I will define what Banded Unlink Diagrams are, and how they are used to describe knotted surfaces in 4-space.
10-16-24
4:30-5:20
Speaker: Austin Crabtree
Abstract: This talk will be an introduction to knot theory, with intent to define and show examples of Vassiliev Invariants.
10-9-24
4:30-5:20
Speaker: Malcolm Gabbard
Abstract:
A way of depicting and understanding 4-manifolds diagrammatically is through Kirby diagrams. I will give a brief overview of the basics of Kirby diagrams and Kirby calculus, how to modify Kirby diagrams to produce equivalent (diffeomorphic) manifolds. Then, using these concepts, I will introduce a knot invariant called the shake slice genus.
9-25-24
4:30-5:20
Speaker: Cael Harris
Abstract:
We will continue our discussion about connections, keeping with our example on S^2, and then define associated bundles, the exterior covariant derivative, and curvature.
9-18-24
4:30-5:20
Speaker: Cael Harris
Abstract: In this talk, I will introduce some of the important machinery needed to do gauge theory, in particular, what is a connection on a principal bundle? We will look at (at least) one important example of a connection, build up some intuition, and then formally define what they are. This can potentially become a series of several talks for the student topology seminar this semester, where we can build up to discuss some more specific examples of important gauge theories such as Yang-Mills, Chern-Simons, Seiberg-Witten, etc.
9-11-24
4:30-5:20
Speaker: Jesse Osnes
Abstract: You can think of the Brown Invariant as the natural next step from the Arf Invariant. That is, the Brown Invariant is able to study non-orientable surfaces, while the Arf Invariant is not. In this talk, I will discuss how Brown is defined and what it measures.
9-4-24
4:30-5:20
Speaker: Jesse Osnes
Abstract: The Arf invariant is used when considering surfaces embedded in four manifolds. In this talk, I will walk through how this invariant is defined.