Title: Ribbon disk formulae for the $\alpha_2$- and $\alpha_3$-invariants of ribbon $2$-knots 

Abstract: Finite type invariants for classical knots have been extended to ribbon $2$-knots, and various related studies have been developed. In this talk, we focus on the degree $2$ and $3$ finite type invariants derived from the Alexander polynomial, called the $\alpha_2$- and $\alpha_3$-invariants, and present explicit formulae for these invariants in terms of ribbon disks. We will begin with the Gauss diagram formula for the second coefficient of the Conway polynomial of a classical knot, and then introduce ribbon $2$-knots, ribbon disks, and their Gauss diagrams. Some examples will also be given. 

Title: Yang-Baxter cohomology and the Zamolodchikov tetrahedron equation

Abstract: In this talk, I will discuss some recent applications of Yang-Baxter cohomology to the construction of solutions to the Zamolodchikov tetrahedron equation, and how these can be used in low-dimensional topology. I will present some connections with computational physics and topological quantum field theory, along with the construction of some quantum invariants in dimensions $3$ and $4$. 

Title: An Interesting Class of Nilpotent Lie Algebras

Abstract: We discuss a new class of nilpotent algebras.  We describe connections to problems in linear dating back to the 1970s.  We present examples, state obstructions to existence, describe structure and give geometric applications.