Jun Murakami - Knot complement and complexified polyhedron - IPAM at UCLA
Recorded 13 October 2026. Jun Murakami of Waseda University presents "Knot complement and complexified polyhedron" at IPAM's Hyperbolic Structures and Quantum Invariants Workshop.Abstract: The complement of a fully augmented hyperbolic link is known to decompose into two identical, totally geodesic, right-angled ideal polyhedra, denoted by P. Let K be a hyperbolic link obtained by performing (p, 1) surgery on the crossing circles. Then, the complement of K can be viewed as the union of two identical deformations of P, which we call the "complexified polyhedron." Here, the edges are parameterized by the eigenvalues of certain elements in the knot group. This approach suggests a new method for proving the volume conjecture by using the Kirillov–Reshetikhin invariant of spatial graphs.
Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-i-hyperbolic-structures-and-quantum-invariants/?tab=overview Receive SMS online on sms24.me
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