|Office ||IPAM 1129
|E-Mail ||chparkin at math .ucla .edu
- About Me
My name is Christian Parkinson. I am a fifth year graduate student in the Mathematics department at UCLA
specializing in applied mathematics. Currently I am working on a project with
Andrea Bertozzi and
wherein we are applying level set methods to problems in environmental crime modeling (poaching and deforestation), and optimal path planning.
Before coming to UCLA, I received my BS and MS in Computational and Applied Mathematics at the
Colorado School of Mines in Golden, Colorado. For my
Master's thesis, I studied mathematical modeling
of in-host HIV dynamics with spatial aspects under the advice of
Since August 2015, I have lived in Los Angeles.
My hobbies include books, movies, TV, trivia, retro video games (particularly SNES) and generally
For professional/academic information, please download my CV in long or short form:
- Research Interests
- Applied Mathematics & Mathematical Modeling with ODE and PDE
- Level Set Methods & Hamilton-Jacobi Type Equations
- Numerical Simulation of ODE and PDE
- Qualifying Exams
- Basic Exam (F15) [While studying for the basic exam, I found it helpful to type up solutions to the problems.
Most problems from exams leading up to my own exam (in Fall 2015) are included. The solutions can be found here:
There are sure to be plenty of typos and a few errors in these solutions; trust them at
your own risk!]
- Numerical Analysis (S16)
- Applied Differential Equations (F16)
- "Modeling Illegal Logging in Brazil," B. Chen, K. Peng, C. Parkinson, A. L. Bertozzi, T. L. Slough, J. Urpelainen. Submitted.
- "A Rotating-Grid Upwind Fast Sweeping Scheme for a Class of Hamilton-Jacobi Equations," C. Parkinson. Submitted to the Journal of Scientific Computing preprint version.
- "A Hamilton-Jacobi Formulation for Time-Optimal Paths of Rectangular Nonholonomic Vehicles," C. Parkinson, A.L. Bertozzi and S. Osher. Submitted to 59th IEEE Conference on Decision and Control preprint version.
- "A Model for Optimal Human Navigation with Stochastic Effects," C. Parkinson, A. L. Bertozzi, D. Arnold and S. Osher. Accepted for publication in the SIAM Journal on Applied Mathematics preprint version
- "Matrix Completion with Selective Sampling," C. Parkinson, K. Huynh, D. Needell. 13th International Conference on Sampling Theory and Applications (SampTA), Bordeaux, France, 2019, pp. 1-4. preprint version
- "Modeling Environmental Crime in Protected Areas Using the Level Set Method," D. Arnold, D. Fernandez, R. Jia, C. Parkinson, D. Tonne, Y. Yaniv, A. L. Bertozzi and S. Osher. SIAM Journal on Applied Mathematics, 79 (2019), no. 3, 802-821. preprint version
- "Optimal Human Navigation in Steep Terrain: A Hamilton-Jacobi-Bellman Approach," C. Parkinson, D. Arnold, A. L. Bertozzi, Y. T. Chow and S. Osher. Communications in Mathematical Sciences, 17 (2019), 227-242. preprint version
- "Mathematical Analysis of an in-host Model of Viral Dynamics with Spatial Heterogeneity," S. Pankavich and C. Parkinson. Discrete and Continuous Dynamical Systems B. 21 (5): 1237-1257 (2016) preprint version