Geometric Analysis and Topology Seminar

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Extrinsic systole and knot distortion

Speaker: Sahana Vasudevan, IAS

Location: Warren Weaver Hall 512

Date: Friday, October 10, 2025, 11 a.m.

Synopsis:

Given a surface embedded in R^3, the extrinsic systole is the diameter of the smallest ball in R^3 that contains a non-contractible closed curve on the surface. I will describe some results about the extrinsic systole of surfaces. I will also explain how extrinsic systole is related to knot distortion, a geometric knot invariant introduced by Gromov in the 1980s; this perspective leads to new lower bounds for the distortion of certain knots.