Discovery Magazine

REU Site: Partial Differential Equations and Dynamical Systems

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. It will be directed by Principal Investigator Ugur Abdulla and two faculty members, and assisted by three graduate students.

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.

Development and investigation of the nonlinear models of the mathematical physics is one of the most important problems of the modern science. Research of nonlinear partial differential equations will provide undergraduate students with an effective introduction to some crucial concepts and methods of nonlinear science, such as the existence of free boundaries and the occurrence of regularity thresholds.The project on optimal control and inverse problems will shed light into modeling and control of important class of nonlinear processes with phase transition, so called free boundary problems, arising in thermophysics and mechanics of continuous media, bioengineering and materials science. Research on dynamical systems and chaos theory will lead students into the fascinating chaos phenomena. Students will be guided through implementation of theoretical methods, such as topological dynamics and graph theory, as well as numerical analysis to discover the universal mechanisms of transition from chaotic to periodic behaviour and vice versa. 

The REU aims to train a new generation of well-rounded mathematicians to shed light on the mathematical problems which arise by modeling complex real life problems, and attacking them with the complementary tools of theoretical and numerical analysis. Students will work on a cutting edge research problem with potential opportunities of new discoveries in the field. All the students will be prepared to present their research results in national conferences and to publish research papers in high level mathematical journals. The proposed REU program is designed to form a research/professional network between students and the faculty advisors which is expected to remain active for several years after the program. The REU Site will facilitate a transition from undergraduate to graduate studies in research careers and inform students about job opportunities that are at the intersection of applied mathematics and STEM disciplines.

An REU program will create a great opportunity for FIT graduate students to mentor advanced undergraduate students in research topics on the frontier of modern applied mathematics. Through dissemination of the cutting edge knowledge they will develop outstanding mentoring and leadership skills, which will tremendously impact their chances to be successful in their future career in academia or industry.