Welcome to my Mathematical Blog . The purpose is to share updates in my research, discussion of mathematical ideas in the fields of my research expertise, discussion of open problems, updates and discussions on my new papers and posted lectures, and in general discussion of any math related topics. It is open to everyone in the mathematical community worldwide.
In particular, this is the weblog for the Research Experience for Undergraduates (REU) Site on Partial Differential Equations and Dynamical Systems, which I am running for 2014-2016 with the grant from the US National Science Foundation. For application, grant, and program information, please see the REU Main Page.
Each summer from 2014 to 2016, 9 undergraduate students will participate in an 8 week summer REU Site on Partial Differential Equations and Dynamical Systems held at the Florida Institute of Technology Mathematical Sciences Department.
The REU Site is designed to involve undergraduate students in innovative research in nonlinear partial differential equations, optimal control and inverse problems for systems with distributed parameters, and dynamical systems and chaos theory, while utilizing modern tools of mathematical and numerical analysis. Students will have a great opportunity to pursue hands-on, original research on the frontier of modern mathematics, which will include the evolution of interfaces for nonlinear reaction-diffusion-convection equations, inverse free boundary problems and optimal control of phase transition processes, and the fine classification of minimal periodic orbits of discrete dynamical systems with application in chaos theory.
For more information on the REU faculty and program, see Dr. Abdulla’s REU page. For an extended description and other related links, see the FIT Research Portal. I will post here periodically both before, during, and after the REU to communicate with other students and the community at large about our results and other interesting information.
Students worked in there groups working on Nonlinear Partial Differential Equations, Optimal Control and Inverse Problems and Dynamical Systems and Chaos Theory. All 10 students are selected as presenters in YMC-2014 in Ohio State University, August 22-24, 2014. Here is the link to abstracts of all three presentations.
Analysis of Interfaces for the Nonlinear Diffusion Equation with Linear Convection by Taylor P Schluter & Lauren T Lanier & Kev Johnson
On the Structure of Minimal $4(2k+1)$-orbits of Continuous Endomorphisms and Universality in Chaos by
Rashad U Abdulla & Batul Kanawati & Anders Ruden
On Some Inverse Free Boundary Problems for Second Order Parabolic PDEs by
Nicholas Crispi & Daniel Kassler & Paige Williams & Bruno Poggi & Scott Pelton-Stroud
Attached youtube video features final presentations by students at the end of the summer session of 2014.