A proof of Gromov's distortion conjecture, d'après John Pardon

The Gromov distortion of a knot K in R^3 is by definition
the maximum ratio of distance along K to Euclidean distance in \R^3.
Given a topological knot type, one then looks at its minimal (or perhaps
infimal) distortion over all positions in R^3.  In 1983, Gromov conjectured
that minimum distortion is unbounded by tame knots.  In particular, he
conjectured that the minimum distortion of a torus knot T(p,q) goes to
infinity as both parameters go to infinity.  I will discuss why the Gromov
distortion conjecture is an interesting and difficult question and, for
the main attraction, I will discuss an exciting proof of the conjecture
by John Pardon of Princeton University.