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;
- 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;
- 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.