PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Federico Rodriguez Hertz, Stephanie Zerby, Anatole Katok, Boris Kalinin.

Title:Singularly beautiful algebraic curves
Seminar:Center for Dynamics and Geometry Seminars
Speaker:Joel Langer, Case Western Reserve University
Abstract:
The theorems of Gauss on constructible n-gons and Abel on uniform subdivision of the Bernoulli lemniscate place the circle and lemniscate among only a handful of algebraic curves known to possess such nice subdivision properties. For these curves, unit speed parameterization (or its norm) extends to meromorphic (elementary or elliptic) functions on the complex plane. Such parameterizations are already rare, as may be seen from the polyhedral geometry on a (complex) curve C; this is de ned via the quadratic di erential on C induced by dx^2 +dy^2. The required behavior of this quadratic di erential forces rather special singularities of C and it follows, e.g., that Bernoulli lemniscates are the only curves of degree at most four with compact polyhedral geometry. In this talk, such results and related examples will be illustrated via a graphical technique for visualizing the (real) foci and polyhedral geometry of an algebraic curve.

Room Reservation Information

Room Number:MB114
Date:05 / 08 / 2013
Time:03:35pm - 04:35pm