Math Colloquium: Eigenmirrors and Eigensurfaces

Wednesday, October 21, 2020

3:00 PM-4:00 PM

R. Andrew Hicks, PhD, Drexel University

Abstract: We call a surface that appears undistorted when viewed in a curved mirror an {\em eigensurface}, and the mirror an {\em eigenmirror}. Such pairs are described by a first-order nonlinear partial differential equation of the form $ a_0 + a_{1}u_{x} + a_{2}u_{y} + a_{3}u_{x}u_{y} + a_{4}u_{x}^{2} + a_{5}u_{y}^{2} = 0$, where $a_{i}=a_{i}(x,y,u)$, which we call the {\em anti-eikonal equation}. We give examples of symbolic and numerical solutions, including pairs that are geometrically congruent. Ray tracing simulations are included that visually confirm the unusual properties of these surfaces.

Contact Information

Georgi Medvedev
gsm29@drexel.edu