For more information about this meeting, contact Federico Rodriguez Hertz, Anatole Katok.
|Title:||Singularly beautiful algebraic curves|
|Seminar:||Center for Dynamics and Geometry Seminar|
|Speaker:||Joel Langer, Case Western Reserve University|
|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 dened via the quadratic dierential on C induced by dx^2 +dy^2.
The required behavior of this quadratic dierential 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
|Date:||05 / 08 / 2013|
|Time:||03:35pm - 04:35pm|