Fonseka, Nalin

Assistant Professor of Mathematics
School of Arts and Sciences
Deeds Hall D318
PhD in Computational Mathematics, The University of North Carolina at Greensboro 2020
MA in Mathematics, Eastern Illinois University 2015
BS in Mathematics (Special degree in Mathematics), University of Peradeniya 2009

About

Dr. Nalin Fonseka joined Carolina University as an assistant professor of mathematics in the School of Arts and Sciences in Fall 2020. After receiving his bachelor’s degree from the University of Peradeniya, Sri Lanka in 2009, he has served as a lecturer at University of Peradeniya from 2010 to 2014. He earned his master’s degree in pure mathematics from Eastern Illinois University in 2015. He received his PhD in computational mathematics from the University of North Carolina at Greensboro in 2020 where he served as a teaching assistant for five years. He has taught various undergraduate mathematics classes since 2010 including hybrid and online classes. His research focuses on Differential Equations (Nonlinear Elliptic Boundary Value Problems) and Mathematical Ecology (Steady State Reaction-Diffusion Equations modeling population dynamics, including the density-dependent dispersal on the boundary and effects of exterior matrix hostility). His research work has resulted in articles published in several journals including the Journal of Mathematical Analysis and Applications, Discrete and Continuous Dynamical Systems, Series S, and Mathematical Biosciences and Engineering. To date, Dr. Nalin Fonseka has collaborated with over 8 researchers including a renowned ecologist.

Personal Website

Publications

N. Fonseka, R. Shivaji, B. Son, and K. Spetzer, Classes of reaction-diffusion equations where a parameter influences the equation as well as the boundary condition, J. Math. Anal. Appl., 476 (2019), no. 2, 480-494.

N. Fonseka, J. Goddard II, Q. Morris, R. Shivaji, and B. Son, On the effects of the exterior matrix hostility and a U-shaped density-dependent dispersal on a diffusive logistic growth model, Discrete Contin. Dyn. Syst. Ser. S (accepted 2019).

J. T. Cronin, N. Fonseka, J. Goddard II, J.Leonard, and R. Shivaji, Modeling the effects of density-dependent emigration, weak Allee effects, and matrix hostility on patch-level population persistence, Mathematical Biosciences, and Engineering. (2019), 17(2) : 1718-1742.

N. Fonseka, J. Machado, and R. Shivaji, A study of logistic growth models influenced by the exterior matrix hostility and grazing in an interior patch, Electron J. Qual. Theory Differ. Equ.  (2020), No. 17, 1-11.

N. Fonseka, A. Muthunayake, R. Shivaji, and B. Son, Singular reaction-diffusion equations where a parameter influences the reaction term and the boundary condition, Topological Methods in Nonlinear Analysis, to appear.

Manuscripts Submitted

N. Fonseka, J. Goddard II, R. Shivaji, and B. Son, A diffusive weak Allee effect model with U-shaped emigration and matrix hostility (Submitted 2020).

A. Acharya, N. Fonseka, and R. Shivaji, Analysis of reaction-diffusion systems where a parameter influences both the reaction terms as well as the boundary (Submitted 2020).

Invited/Contributed Talks

American Mathematical Society (AMS) Annual Meeting, Colorado Convention Center, Denver, CO, Classes of Reaction-Diffusion Equations Where a Parameter Influences the Equation as well as the Boundary Condition, January 2020.

AMS Fall Southeastern Sectional Meeting, University of Florida, Gainesville, FL, Classes of Reaction-Diffusion Equations Where a Parameter Influences the Equation as well as the Boundary Condition, November 2019.

AMS Spring Southeastern Sectional Meeting, Auburn University, Auburn, AL, Classes of Reaction-Diffusion Equations Where a Parameter Influences the Equation as well as the Boundary Condition, March 2019.

The 15th Annual UNCG Regional Mathematics and Statistics Conference, UNCG, Greensboro, NC, On the effects of the exterior matrix hostility and a U-shaped density-dependent dispersal on a diffusive logistic growth model, November 2019.

The 39th Southeastern-Atlantic Regional Conference on Differential Equations (SEARCDE), Embry-Riddle Aeronautical University, Daytona Beach, FL, Singular reaction-diffusion equations where a parameter influences the reaction term and the boundary condition, October 2019.

The 14th Annual UNCG Regional Mathematics and Statistics Conference, UNCG, Greensboro, NC, Analysis of positive solutions for a logistic growth model with grazing, November 2018.

The 38th SEARCDE, University of North Georgia, Gainesville, GA, Classes of Reaction-Diffusion Equations Where a Parameter Influences the Equation as well as the Boundary Condition, October 2018.

Courses Taught

  • Basic Mathematics
  • College Algebra
  • Precalculus I, II
  • Calculus I, II
  • Calculus w/ Business Applications
  • Contemporary Topics in Mathematics
Fonseka, Nalin