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Math Colloquium: Eigenmirrors and Eigensurfaces
Start Date: 10/21/2020Start Time: 3:00 PM
End Date: 10/21/2020End Time: 4:00 PM

Event Description

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:
Name: Georgi Medvedev
Email: gsm29@drexel.edu
Online Zoom Meeting
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