Independent Study Opportunities

I am broadly interested in the applications of mathematical analysis, differential geometry, and numerical analysis in the study of differential equations and optimization problems that appear in physics and engineering.

Skills that are useful for undergraduates who want to do an independent study project with me:

• 1- Linear Algebra (Math 100)
• 2- Multivariable Calculus (Math 32, Math 105A)
• 3- Differential Equations (Math 45, Math 105B)
• 4- Differential Geometry
• 5- Mathematical Analysis (Math 130A, Math 130B)

Topics

Here is a list of topics (some are very general, and some are more specific) that can serve as a guide to develop a research project or an independent study project. If any of these topics interests you, and you would like to talk with me about the topics in which you are interested, please send me an email.
• Discrete Fourier Transform
• Geometric Integrators
• The ODE Solvers in MATLAB
• Stability of Numerical Methods for ODEs
• Numerical Simulation of Stochastic Differential Equations
• Operator Splitting
• Krylov Subspace Methods
• Singular Value Decomposition
• Principal Component Analysis
• Algebraic Multigrid Methods
• Meshfree Methods
• Shape Differential Calculus
• Discrete Differential Geometry
• Stefan Problem
• What is a wavelet?
• What is a stiff differential equation?
• Distribution Theory
• Spectral Methods
• Mathematical Models of Cellular Membranes
• Mathematical Foundations of Elasticity
• Geometric Mechanics
• Finite Element Exterior Calculus
• Markov State Models
• Global Existence in Reaction-Diffusion Systems
• Symmetry and Gauge Freedom
• Positive Scalar Curvature and Applications
• The Yamabe Problem
• The Initial Value Problem in General Relativity
• Stochastic Simulations of Reaction-Diffusion Processes
• Monte Carlo Integration