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RESEARCH INTERESTS
RESEARCH INTERESTS
I am interested in studying steady state reaction diffusion equations arising in mathematical biology and elliptic partial differential equations and systems.
I am interested in studying steady state reaction diffusion equations arising in mathematical biology and elliptic partial differential equations and systems.
Prof. Ratnasingham Shivaji was my advisor. I studied steady state reaction diffusion equations under his direction.
My current research focus is on studying the structure of positive solutions of steady state reaction diffusion equations which arise in ecology. Our studies include logistic growth models, weak Allee growth models, and grazing models where a parameter influences the equation as well as the boundary conditions. Many of the ecological research projects I worked on have been supported by my advisor's NSF grant. I am also interested in studying the existence multiplicity and uniqueness of positive solutions to elliptic partial differential equations and systems.
Mathematical Biology
Mathematical Biology
Mathematical biology is the use of mathematical tools to study biological systems. Mathematical biology focuses on the mathematical representation and modeling of biological processes, using techniques and tools of applied mathematics. Describing systems in a quantitative manner means their behavior can be better studied, and hence properties can be predicted that might not be evident to the experimenter. This requires precise mathematical models. Mathematical biology employs many components of mathematics, and has contributed to the development of new techniques. In particular, elliptic partial differential equations can be used to model the population density of a certain species living in a habitat surrounded by a hostile environment. These models can be studied and make predictions on population persistence and understand the effects of the matrix hostility on the steady states.
A weak Allee model arising in population dynamics
A steady state reaction diffusion equation where a parameter influences the equation as well as the boundary conditions.
A grazing model arising in ecological systems
A recent research work: An establishment of a Sigma-shaped bifurcation curve for a class of reaction-diffusion equations.
A recent research work: An establishment of a Sigma-shaped bifurcation curve for a class of reaction-diffusion equations.
Conference Talks
Conference Talks
Presenting a talk at JMM, Boston, MA, January 2023.
University of Massachusetts-Amherst, Amherst, MA (Fall Eastern Sectional Meeting - October 2022)
Presenting a talk at 38th SEARCDE, University of North Georgia, Gainesville, 2018
Presenting summer research work on "Singular reaction diffusion equations where the parameter influences the boundary"at UNCG, 2019
Presenting a talk at AMS Spring Southeastern Sectional Meeting, University of Florida, Gainesville, FL, November 2019.
Plenary Talks
Plenary Talks
UCM Scholars Symposium, University of Central Missouri, Warrensburg, MO, April 2024.
Colloquium/Seminar Talks
Colloquium/Seminar Talks
Appalachian State University, Boone, NC, November 2022.
Wake Forest University, Winston Salem, NC, September 2023.
University of Tennessee at Martin, TN, September 2024.
Iowa State University, IA, September 2024.
Invited Talks
Invited Talks
American Mathematical Society (AMS) Spring Southeastern Sectional Meeting, Auburn University, Auburn, AL, March 2019.
AMS Spring Southeastern Sectional Meeting, University of Florida, Gainesville, FL, November 2019.
AMS Annual Meeting, Colorado Convention Center, Denver, CO, January 2020.
AMS Fall Southeastern Sectional Meeting (virtual meeting), October 2020.
AMS Fall Western Sectional Meeting (virtual meeting), October 2020.
AMS Annual Meeting (virtual meeting), January 2021.
AMS Spring Eastern Sectional Meeting (virtual meeting), March 2021.
AMS Fall Central Virtual Sectional Meeting (virtual meeting), October 2021.
AMS Fall Eastern Sectional Meeting, University of Massachusetts-Amherst, Amherst, MA, October 2022.
AMS Fall Southeastern Sectional Meeting, the University of Tennessee at Chattanooga, Chattanooga, TN, October 2022.
AMS Annual Meeting, John B. Hynes Veterans Memorial Convention Center, Boston, MA, January 2023.
AMS Fall Central Sectional Meeting, Creighton University, Omaha, NE, October 2023.
AMS Annual Meeting, Moscone Center, San Francisco, CA, January 2024.
AMS Annual Meeting, Sheraton Grand Seattle, Seattle Convention, Seattle, WA, January 2025.
AMS Spring Central Sectional Meeting, March 2025.
AMS Fall Central Sectional Meeting, October 2025.
Contributed Talks
Contributed Talks
The 15th Annual UNCG Regional Mathematics and Statistics Conference, University of North Carolina at Greensboro, Greensboro, NC, November 2019.
The 39th Southeastern-Atlantic Regional Conference on Differential Equations, Embry-Riddle Aeronautical University, Daytona Beach, FL, October 2019.
The 14th Annual UNCG Regional Mathematics and Statistics Conference, University of North Carolina at Greensboro, Greensboro, NC, November 2018.
The 38th Southeastern-Atlantic Regional Conference on Differential Equations, University of North Georgia, Gainesville, GA, October 2018.
9th International Online Conference on Mathematical Analysis, Differential Equation \& Applications (MADEA 9), June 2021.
UNC Greensboro PDE Conference of 2021, University of North Carolina at Greensboro, Greensboro, NC, July 2021.
The 40th Southeastern-Atlantic Regional Conference on Differential Equations, NC State University, Raleigh, NA, November 2022.
MAA Southeastern Section Meeting, Coastal Carolina University, Conway, NC, March 2023.
MAA Missouri Section Meeting, William Jewell College, Liberty, MO, April 2024.
International Conference on Differential Equations (ICDE), Florida Gulf Coast University, Fort Myers, FL, June 2024.
MAA Missouri Section Meeting, Saint Louis University, Saint Louis, MO, April 2025.
Missouri Academy of Science 62nd Annual Meeting, University of Central Missouri, Warrensburg, MO, April 2025.
UNC Greensboro PDE Conference of 2025, University of North Carolina at Greensboro, Greensboro, NC, October 2025.
International Conference Talks
International Conference Talks
9th International Online Conference on mathematical analysis, differential equation & applications (MADEA 9), June 2021.
10th international eurasian conference on mathematical sciences and applications (IECMSA), August 2021.
5th International Conference on Mathematics (ICOM 2021), December 2021.
III International Conference on Mathematics and its Applications in Science and Engineering (ICMASE 2022), July 2022.
SIMIODE EXPO 2024 online international conference, February 2024.
SOME RECORDED TALKS
SOME RECORDED TALKS
AMS March 2021.mp4Presenting a talk at AMS Spring Eastern Sectional Meeting (virtual), March 2021.
20191103_093409.mp4Presenting a talk at AMS Spring Southeastern Sectional Meeting, University of Florida, Gainesville, FL, November 2019.
SEARCDE Talk.MOVPresenting a talk at 38th SEARCDE, University of North Georgia, Gainesville, October 2018
AMS Talk (1).mp4Presenting a talk at AMS Fall Southeastern Sectional Meeting (virtual), October 2020.
Talk.mp4Presenting a talk at AMS Fall Western Sectional Meeting (virtual), October 2020.
COLLABORATORS
COLLABORATORS
At AMS Annual Meeting, Moscone Center, San Francisco, CA, January 2024.
At the 39th SEARCDE hosted by the Department of Mathematics, Embry-Riddle Aeronautical University, Daytona Beach, Florida, 2019.
At the 13th Annual Graduate Student Topology and Geometry Conference, University of Illinois, Urbana-Champaign, IL, March 2015
LIST OF PUBLICATIONS
LIST OF PUBLICATIONS
List_of_Publications_Fonseka__.pdfElectronic files of some of the publications
Electronic files of some of the publications
Fonseka_1_JMAA_.pdfFonseka_2_DCDS_S_.pdfFonseka_3_MBE_.pdfFonseka_4_EJQTDE_.pdfFonseka_5_TMNA_.pdfFonseka_6_DCDS_B_.pdfFonseka_7_BVP_.pdfFonseka_8_ANONA_.pdf
Poster presentation SIAM – PD, March 2022.
A picnic after the the conference on Variational and Topological Methods: Theory, Applications, Numerical Simulations, and Open Problems, Northern Arizona University, Flagstaff, 2018
At a dinner while attending the AMS Spring Southeastern Sectional Meeting, Auburn University, Auburn, 2019
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