Talks given by external students/researchers during the year 2026 are listed below.

Fall 2026

EP2605: Smallest volume hyperbolic link complement with n components

• Speaker: Shashank Gupta, IISER Mohali
• Abstract: In 2001, Cao and Meyerhoff proved that the smallest volume hyperbolic link complement with one cusp is the figure-8 knot complement. Agol posed a generalisation of this as a question: what is the smallest volume hyperbolic link complement with n components? In his thesis, Venzke proposed an answer to Agol’s question, arguing that the volume for n ≥ 11 is beaten by the $(n-1)$ fold cyclic cover of the Whitehead link complement. But this was without proof until Kaiser-Purcell-Rollins proved Venzke’s statement for $n \geq 60$. In this talk, I will discuss the original conjecture of Agol which states that minimally twisted chain links are the smallest volume hyperbolic n-cusped manifolds. The Kaiser–Purcell–Rollins paper provides computational evidence that they are beaten by the Whitehead cyclic cover, but this is not a complete proof showing that the chain link is globally minimal volume among all $n$-cusped manifolds in these ranges. Even though most data support this numerically, a complete classification or proof is still open for some of these small $n$. Also, a complete classification of minimal volume n-cusped manifolds for $3 \leq n \leq 59$ needs to be given.$w$.
  I will discuss all the possibilities related to this open problem. The talk will start with some preliminaries from hyperbolic knot theory and then lead to this open problem. It may be useful for people who want to work in the vast domain of 3- and 4-dimensional geometry and topology.
• Pre-requisites: Basic knowledge of knot theory, Hyperbolic Geometry
• Video: (Not Recorded)
• Date and Time: Friday (14th August), 4:30 PM to 5:45 PM
• Venue: 008, CR Rao Bhavan