I lucky got the chance to go to the last Geometry and Topology Seminar at CUNY Graduate center on December 11th right before the holidays. It was a treat.
Anastasiia Tsvietkova of Louisiana State University presented her dissertation entitled Hyperbolic Structures from Link Diagrams.
Rooted in knot theory and geometric topology, she builds upon W. Thurston’s Hyperbolization Theorem,
which demonstrates that every link in a 3-sphere is
a torus link,
a satellite link
or a hyperbolic link
and these three categories are mutually exclusive. That just SOUNDS satisfying.
Her dissertation lays out an alternative way to compute the hyperbolic link in a 2-DIMENSIONAL PROJECTION.
That deserves a “WOW!”
I enjoyed the talk very much, even though much of the math was over my head.
The fact that the whole lecture only dealt with 3-dimensions made it easier.
I, at least, understood what was at stake and enjoyed following
the structure of the argument.
You can read her paper.
The bottom line:
The lecture got me to open my Knot Theory book and
revisit my drawings of hyperbolic paraboloidal shapes
from Calculus III,
because knot theory is fun and I enjoy calculus.