Current Projects:

4D Scene Reconstruction; Single-Step Flow Matching; Motion Prediction and Simulation

Advisor: Prof. Rafael de la Llave, Georgia Institute of Technology

* Developed an iterative algorithm for computing the invariant manifolds and the corresponding isochrons for 2-dim dynamical systems using the parameterization method.

* Proved the theory of convergence in an a-posteriori format using Nash- Moser smoothing technique. Implemented the algorithm for the dissipative standard map and explored scenarios near the breakdown.

* The algorithm is irrespective of the dynamics on the invariant circle (rotation or phase-locked). It has an almost quadratic convergence rate and can work even near the breakdown.

Instructor for Introduction to Probability and Statistics and Differential Equations.

Teaching/Lecture Assistant for Probability and Statistics with Applications, Differential Equations, Differential Calculus, Multivariable Calculus, and Multivariable Calculus.

* Built a predator-prey interaction model with refuge and allee effect. Proved the existence and the uniform boundedness of the solution, and analyzed the stability of the equilibria.

* Studied the global dynamics of the model and the existence of center manifold and Hopf Bifurcation, explored the biomass ratio.