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
Friday August 30

4-5pm Crawford 210

no talk
Friday September 6

4-5pm Crawford 210

Dr. Ugur Abdulla

Florida Institute of Technology

Department of Mathematical Sciences

Title: Introduction to Nonlinear PDEs I

Abstract: PDEs arising in a majority of real world applications are nonlinear. Despite the complexity of the theory of nonlinear PDEs, one can observe key equations or systems which are essential for developing the theory for a particular class of PDEs. In three introductory lectures, I will concentrate on one of those key equations, so called nonlinear diffusion equation. I will outline the historical development of the fascinating world of nonlinear PDEs, introduce some crucial concepts and methods of nonlinear science, and discuss the perspectives of future development. At the end of my third lecture I will formulate some open problems for PhD Dissertation research. Lectures will be accessible to graduate students in Applied Mathematics, Operations Research, Physics and those Engineering majors whose research field involve PDEs. They will also be accessible to undergraduate students who succeded in MTH3210.

Friday September 13

4-5pm Crawford 210

Dr. Ugur Abdulla

Florida Institute of Technology

Department of Mathematical Sciences

Title: Introduction to Nonlinear PDEs II
Friday September 20

4-5pm Crawford 210

Max Goldfarb

Florida Institute of Technology

Department of Mathematical Sciences

Title: On the evolution of the interfaces for the nonlinear reaction-diffusion type equations.

Abstract: In this talk I address the Barenblatt's problem about the short-time evolution of the interfaces and local solutions of the nonlinear degenerate parabolic equations of the reaction-diffusion type. A full solution of the Barenblatt problem for the reaction-diffusion equation was given in two papers: Abdulla & King, SIAM J. Math. Anal., 23,2(2000), 235-260; and Abdulla, Nonlinear Analysis, 50,4(2002), 541-560. The problem remains open for the diffusion-convection case.

In this work, a first step towards solving this problem is made: one region of the parameter space is identified where the interface expands, and a borderline case in which the solution is self-similar is also identified. A significant part of this research is based on numerical computation and I will demonstrate the numerical results along with discussion of major difficulties.

Friday September 27

4-5pm Crawford 210

Bruno Poggi

Florida Institute of Technology

Department of Mathematical Sciences

Title: Proof of the existence and uniqueness theorem for a normal system of ODEs

Abstract: Proof of the existence and uniqueness theorem for a normal system of ordinary differential equations will be presented by using only calculus tools. Talk will be accessible to undergraduate and graduate students.

Friday October 4

4-5pm Crawford 210

Dr. Ugur Abdulla

Florida Institute of Technology

Department of Mathematical Sciences

Title: Introduction to Nonlinear PDEs III

Abstract: PDEs arising in a majority of real world applications are nonlinear. Despite the complexity of the theory of nonlinear PDEs, one can observe key equations or systems which are essential for developing the theory for a particular class of PDEs. In three introductory lectures, I will concentrate on one of those key equations, so called nonlinear diffusion equation. I will outline the historical development of the fascinating world of nonlinear PDEs, introduce some crucial concepts and methods of nonlinear science, and discuss the perspectives of future development. At the end of my third lecture I will formulate some open problems for PhD Dissertation research. Lectures will be accessible to graduate students in Applied Mathematics, Operations Research, Physics and those Engineering majors whose research field involve PDEs. They will also be accessible to undergraduate students who succeded in MTH3210.

Friday October 11

4-5pm Crawford 210

no talk
Friday October 18

4-5pm Crawford 210

Naveed Iqbal

Florida Institute of Technology

Department of Mathematical Science

Title: Proof of the Sharkovskii's Theorem

Abstract: Talk will present the proof of the Sharkovski's striking theorem on the description and hierarchy of all possible sets of periods, for the periodic trajectories of a continuous map of an interval. Talk will be accessible to graduate and advanced undergraduate students.

Friday October 25

4-5pm Crawford 210

no talk no talk
Friday November 1

4-5pm Crawford 210

no talk no talk
Friday November 8

4-5pm Crawford 210

Dr. O'Neil Smith

Harris Corporation

SIAM Speaker

Title: Category Space Dimensionality Reduction for Supervised Learning

Abstract: This research investigates the reasons that make the multiclass classification problem difficult, and suggest that category ambiguity is at the heart of the problem. The essential concepts have been neglected because in the past, classes were perceived to be independent. This leads to limited approaches in which techniques assume distinct classes and assign nominal labels to them. We argue that class relationships exist that must be exploited. The approach I propose gives an alternate method for dimensionality reduction so that multiclass classification techniques can overcome several of the problems that exis with pair wise classification schemes and exhibits better performance on many problems. We look to separate objects according to similar qualities and characteristics by projecting to a space – a Category Space – defined by the number of classes and the properties of the classes. After dimensionality reduction to the category space, we use a classification technique to evaluate performance on a large collection of benchmark data sets.

Friday November 15

4-5pm Crawford 210

Joao Alberta de Faria

Florida Institute of Technology

Department of Mathematical Sciences

Title: Cycles on Wehler K3 Surfaces

Abstract: This talks discusses the dynamics of a particular class of reversible maps that arise as automorphisms of a K3 surface. We are interested mainly in the distribution of cycle lengths when the surface is defined over a finite field (i.e. the map has a finite phase space). In the particular situation where the map is a composition of two involutions, as is the case for our K3 surfaces, Roberts-Vivaldi give a combinatorial description of the cycle distribution if the fixed points of the involutions satisfy certain properties. We demonstrate that their hypotheses hold for this class of K3 surfaces.

Friday November 22

4-5pm Crawford 210

Dr. Donald Richardson

Florida Institute of Technology

Department of Mathematical Sciences

Title: Permutation Polynomials

Abstract: A brief discussion of finite fields and permutation polynomials, with emphasis on the Dickson Polynomials and their applications in Cryptography.

Friday November 29

4-5pm Crawford 210

no talk.
Friday December 6

4-5pm Crawford 210

Dr. Eugene Demidenko

Professor of Biostatistics and Epidemiology

Geisel school of Medicine and Department of Mathematics at Dartmouth College

SIAM Speaker

Past Semesters

Spring 2013

Fall 2012