Undergraduate Summer Research Project

Summer Research Project 2015 (Undergrads)

"Dynamics and Spectral Asymptotics: exploration and visualization"

Delayed until Summer 2015 as currently other financial commitments of my grant don't allow me to contribute the necessary amount to student salary

  • You must satisfy following conditions:
    • You are University of Toronto student enrolled in Math. Specialist program;
    • You are on your second on third year (since project most lokely to be extended beyond Summer);
    • You are familiar with LaTeX and you are ready to learn a lot. You are reliable;
    • You are interested in Analysis;
    • You are available May 1 – August 31, 2015.
    • You need to talk with me not later than January 25, 2015.
  • Assets but not requrements:
    • Using Mac OSX would be an asset;
    • Familiarity with Computer Graphics and Symbolic Calculation software: (Maple/Mathematica, Asymptote);
    • Native English speaker;
  • Details
    • Spectral Asymptotics for Partial Differential Operators are intimately related with classical dynamics;
    • For example for Schrödinger operator we just consider classical Hamiltonians and in the special case of Laplace operator we need to study geodesics;
    • If there is a boundary trajectories reflect from it (sometimes with branching) and billiards come into play;
    • We want to represent qualitive behavior of such billiards through visualization;
  • etc<
    • I am working on my future Monster-size e-Book and need a general technical help;
    • Also lots of interesting examples should be considered;
    • Short description in my talk Spectral Asymptotics and Dynamics;
    • If you are interested you will apply for NSERC Summer Research Grant and I will support your application;
    • There is a possibility of continued less intensive paid work after Summer Research Grant (i.e. September 1, 2015);
    • There is also a possibility of the second Summer Research Project in 2016.