Prof. Chris Bishop (Stony Brook University, U.S.A.)
will speak on
Weil-Peterson Curves, Traveling Salesman Theorems, and Minimal Surfaces
Time: 2:00PM
Date: Fri 27th March 2026
Location: (See abstract)
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Abstract: LOCATION: Icon Theatre D, Science Hub, O'Brien Centre, UCD
Coffee to follow in the room N3.20/N3.21 Science Centre North. If you plan to attend, please complete this brief form.
Weil-Petersson curves are a class of rectifiable closed curves in the plane, defined as the closure of the smooth curves with respect to the Weil-Petersson metric defined by Takhtajan and Teo in 2006. Their work solved a problem from string theory by making the space of closed loops into a Hilbert manifold, but the same class of curves also arises naturally in complex analysis, geometric measure theory, probability theory, knot theory, computer vision, and other areas. No geometric description of Weil-Petersson curves was known until 2019, but there are now more than twenty equivalent conditions. One involves inscribed polygons and can be explained to a calculus student. Another is a strengthening of Peter Jones's traveling salesman condition characterizing rectifiable curves. A third says a curve is Weil-Petersson iff it bounds a minimal surface in hyperbolic 3-space that has finite total curvature. I will discuss these and several other characterizations and sketch why they are all equivalent to each other. The lecture will contain many pictures, several definitions, but not too many technical details.
(This talk is part of the UCD School of Mathematics and Statistics Colloquium series.)
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