Department of Mathematical Sciences

Colloquium Series

Purpose: To discuss mathematical research and interdisciplinary problems in all areas of mathematics and applied mathematics. Talks are welcome from faculty, graduate students, and outside speakers from academia and industry. Talks should be at a level accessible to graduate students. Students and faculty at all levels and from all departments are welcome to attend.

Date/Time Speaker Title/Abstract
Monday May 12

10-11am Crawford 526

Dr. Ugur Abdulla

Department of Mathematical Sciences

Florida Institute of Technology

Title: Optimal Control and Inverse Free Boundary Problems for Parabolic PDEs II

Abstract: In this talk I will present the new variational formulation of the inverse Stefan problem based on the optimal control theory. Presentation will follow my recent paper in Inverse Problems and Imaging, 7, 2(2013), 307-340. I will describe the results on the well-posedness in Sobolev spaces framework and the convergence of discrete optimal control problems to the original problem. I will outline the method of proofs and formulate some open problems for PhD research, as well as research projects for REU Site on PDEs and Dynamical Systems.

Wednesday May 14 10-11am Crawford 526 Dr. Ugur Abdulla

Department of Mathematical Sciences

Florida Institute of Technology

Title: Optimal Control and Inverse Free Boundary Problems for Parabolic PDEs III

Abstract: In this talk I will present the new variational formulation of the inverse Stefan problem based on the optimal control theory. Presentation will follow my recent paper in Inverse Problems and Imaging, 7, 2(2013), 307-340. I will describe the results on the well-posedness in Sobolev spaces framework and the convergence of discrete optimal control problems to the original problem. I will outline the method of proofs and formulate some open problems for PhD research, as well as research projects for REU Site on PDEs and Dynamical Systems.

Friday May 16 10:30-11:30am Crawford 526 Dr. Ugur Abdulla

Department of Mathematical Sciences

Florida Institute of Technology

Title: Optimal Control and Inverse Free Boundary Problems for Parabolic PDEs IV

Abstract: In this talk I will present the new variational formulation of the inverse Stefan problem based on the optimal control theory. Presentation will follow my recent paper in Inverse Problems and Imaging, 7, 2(2013), 307-340. I will describe the results on the well-posedness in Sobolev spaces framework and the convergence of discrete optimal control problems to the original problem. I will outline the method of proofs and formulate some open problems for PhD research, as well as research projects for REU Site on PDEs and Dynamical Systems.

Tuesday May 27 10:30-11:30am Crawford 526 Dr. Ugur Abdulla

Department of Mathematical Sciences

Florida Institute of Technology

Title: Topological Dynamics and Universality in Chaos. I. Sharkovski's Theorem

Abstract: In his celebrated paper Sharkovski discovered a fundamental law on the coexistence of periodic orbits of the continuous maps on the real line. His work is a prelude for the understanding of complex dynamics and chaotic maps. In several talks I am going to present the proof of this remarkable result.

Wednesday May 28 10:30-11:30am Crawford 526 Dr. Ugur Abdulla

Department of Mathematical Sciences

Florida Institute of Technology

Title: Topological Dynamics and Universality in Chaos. II. Sharkovski's Theorem

Abstract: In his celebrated paper Sharkovski discovered a fundamental law on the coexistence of periodic orbits of the continuous maps on the real line. His work is a prelude for the understanding of complex dynamics and chaotic maps. In several talks I am going to present the proof of this remarkable result.

Thursday May 29 10:30-11:30am Crawford 526 Dr. Ugur Abdulla

Department of Mathematical Sciences

Florida Institute of Technology

Title: Topological Dynamics and Universality in Chaos. III. Sharkovski's Theorem

Abstract: In his celebrated paper Sharkovski discovered a fundamental law on the coexistence of periodic orbits of the continuous maps on the real line. His work is a prelude for the understanding of complex dynamics and chaotic maps. In several talks I am going to present the proof of this remarkable result.

Friday May 30 10:30-11:30am Crawford 526 Dr. Ugur Abdulla

Department of Mathematical Sciences

Florida Institute of Technology

Title: Topological Dynamics and Universality in Chaos. IV. Fine Classification of Minimal Orbits

Abstract: In this talk I will present the fine classification of minimal orbits of the continuous endomorphisms on the real line and its role in chaotic dynamics. The lecture will follow more or less out current paper in the Journal of Difference Equations and Applications, 19, 9(2013), 1395-1416. I will formulate some open problems for Ph.D. reserach, as well as research projects for REU site on PDEs and Dynamical Systems.

Past Semesters

Spring 2014

Fall 2013

Spring 2013

Fall 2012