** Splice-unknotting and crosscap numbers.- Thomas Kindred (University of Nebraska at Lincoln)**

Abstract: Ito-Takimura recently introduced the splice-unknotting number of a knot. This diagrammatic invariant provides an upper bound for a knot's crosscap number, with equality in the alternating case. Using results of Kalfagianni-Lee, this equality leads to corollaries regarding hyperbolic volume and the Jones polynomial.

**Families of fundamental shadow links realized as links in $S^3$- Sanjay Kumar (Michigan State University)**

Abstract: In 2015, Chen and Yang provided evidence that the asymptotics of the Turaev-Viro invariant of a hyperbolic $3$-manifold evaluated at the root of unity $\exp(\frac{2\pi i}{r})$ have growth rates given by the hyperbolic volume. This has been proven by Belletti, Detcherry, Kalfagianni, and Yang for an infinite family of hyperbolic links in connect sums of $S^1 \times S^2$ known as the fundamental shadow links. In this talk, I will present examples of links in $S^3$ satisfying the Turaev-Viro invariant volume conjecture through homeomorphisms with complements of fundamental shadow links along with an application towards the conjecture posed by Andersen, Masbaum, and Ueno (AMU conjecture).

**Volume conjecture, geometric decomposition and deformation of hyperbolic structures (I) and (II)- Ka Ho Wong (Texas A & M University)**

(I)

(II)

Abstract: The Chen-Yang volume conjecture of the Turaev-Viro invariant is a new topic in quantum topology. It has been shown that the $(2N+1)$-th Turaev-Viro invariant for a link complement can be expressed as a sum of norm squared of the colored Jones polynomial of the link evaluated at $t=\exp\left(\frac{2\pi i}{ N+\frac{1}{2}}\right)$. This leads to the study of the asymptotics for the $M$-th colored Jones polynomials of links evaluated at $(N+\frac{1}{2})$-th root of unity, with a fixed limiting ratio of $M$ to $N+\frac{1}{2}$. In the first talk, I will recall the definition of the colored Jones polynomials and discuss how the asymptotics of the colored Jones polynomials of the Whitehead link is related to the (not necessarily complete) hyperbolic structures on its complement. Then, in the second talk, we will focus on some satellite links whose complements have more than one hyperbolic piece in the geometric decomposition, and relate the asymptotics of their colored Jones polynomials to the geometric structures on the geometric pieces.