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FrankMath World
- Office: 2202 Mathematical Science
- Office Hours: Tuesday 3:30pm to 5:30pm
- Phone: No Telephone Now
- E-mail : < frankliou@ucdavis.edu>
- MSN:<g913202@oz.nthu.edu.tw>
- Postal Address: Department of Mathematics 1 Shields Ave. University of California
Davis, CA 95616-8633
TA Teaching
2007 Fall Quarter/21B
2007 Winter Quarter/21C
2007 Spring Quarter/16B
Course that I've taken
1. 2007 Fall/Analysis/Math Fluid dynamics/Math Quantum mechanics
2. 2008 Winter/Analysis/Partial Differential Equations/Ordinary Differential Equations
3. 2008 Spring/Analysis/Partial Differential Equations/Differential Topology/Lie groups
Master
Thesis
- Inverse problems of the string with a piecewise density
function. (Preprint)
The
Math Field That I am
Interested with:
- Differential Geometry
- Stochastic Analysis
- Quantum Physics
- C* Algebra and K theory
Lecture Notes
When I was a research asistant
of National Center Theoretical Science in Taiwan, I gave a series of talks
about the analysis on Riemannian Manifolds. What I focused
on were spectral problems on Riemannian manifolds. Before
studying this topic, we need the gradient estimates, the Harnack
inequality, of the Laplace equations on manifolds with possitive Ricci
curvature.
The Harnack Inequality on
manifolds with positive Ricci curvature
I have studied the inverse spectral theory for several years and also
studied the infinite dimensional Hilbert manifolds related to the
inverse spectral theory. The isospectral set of the Schrodinger
equation forms an infinite dimensional submanifold of the Hilbert space
L^2[0,1]. We can construct the local chart to some l^2 space by using
variational calculus. Here is one note about the basic idea of the
construction of local chart.
The Inverse Dirichlet Problem
Some Useful Notel