Nalin Fonseka - MENTORING

undergraduate students

Loren Baker

University of Central Missouri (UCM), graduated in May 2025.
Project title: Reversed Sigma-shaped bifurcation curves for superlinear two-point boundary value problems.
Presented talks at
- KME honor society meeting, April 2025 (titled "Reversed Sigma-shaped bifurcation curves for superlinear two-point boundary value problems").
- MAKO undergraduate mathematics research conference, November 2025 (titled "Reversed Sigma-shaped bifurcation curves for superlinear two-point boundary value problems").
Manuscript titled "Reversed Sigma-shaped bifurcation curves for superlinear two-point boundary value problems" (Submitted 2026).

Undergarduare research student Loren Baker presenting at KME honor society meeting

Blake Ricketson

B.S. in Mathematics and Computer Science, University of Central Missouri (UCM), graduated in May 2025.
Project title: On the structure of positive steady states for an ecological model.
Presented contributed talks at
- the UCM scholars symposium, April 2024 (titled "On the structure of positive steady states to an ecological model").
- the MAA Missouri Section Meeting, April 2024 (titled "A weak Allee growth model arising in mathematical ecology").
Manuscript titled "A bifurcation result for an ecological model via a quadrature method" (Accepted 2024).

Working with Blake Ricketson at UCM

Jackson Leonard

B.S. in Mathematics, UNCG, Graduated in May, 2020.
Presented a talk titled"Bifurcation diagrams for population dynamics models with weak Allee eﬀects and U-shaped density dependent dispersal on the boundary" in 14th Annual UNCG Regional Mathematics and Statistics Conference, University of North Carolina at Greensboro, Greensboro, NC, November 2018.
Manuscript titled "Modeling the effects of density dependent emigration, weak Allee effects, and matrix hostility on patch-level population persistence " (Accepted 2019).

Working with Jackson on a weak Allee model arising in population dynamics

Working with Juan on a linear growth problem

Juan Quiroa

B.S. in Mathematics, UNCG, Graduated in May 2020.
Presented a talk titled "Analysis of Positive Solutions for a Reaction-Diffusion Model where the Reaction Term Grows Linearly at Infinity" in the 14th Annual UNCG Regional Mathematics and Statistics Conference, University of North Carolina at Greensboro, Greensboro, NC, November 2018.
Manuscript titled "Sigma-shaped bifurcation curves " (Accepted 2021).

Jonathan Machado Bilbraut

B.S. in Mathematics, UNCG, graduated in May 2019.
Submitted an honor thesis titled "Bifurcation curves for logistic growth models with grazing on an interior patch" in completion of the undergraduate research project.
Manuscript titled "A study of logistic growth models influenced by the exterior matrix hostility and grazing in an interior patch " (Accepted 2019).

Working with Jonathan on a split domain problem arising in ecology

Sara Feggeler

B.A. in Mathematics, UNCG, graduated in May, 2019.
Presented a talk titled "Bifurcation diagrams for a logistic growth model with grazing" in 14th Annual UNCG Regional Mathematics and Statistics Conference, University of North Carolina at Greensboro, Greensboro, NC, November 2018.

Working on an ecological model with Bryant Bugna.

Bryant Bugna

M.S. in Mathematics, UCM, graduated in May, 2025.
Thesis title "Analysis of bifurcation diagrams for positive solutions for classes of landscape ecological models"
Manuscript titled "Analysis of bifurcation diagrams for positive solutions for classes of landscape ecological models" (Accepted 2025).

Working on a positone problem with Kei Spetzer under Prof. Ratnasingham Shivaji's guidance.

Keri Spetzer

M.A. in Mathematics, UNCG, graduated in May, 2018.
Project title "Positive solutions for a class of nonlinear boundary value problems"
Manuscript titled"Classes of reaction diﬀusion equations where a parameter inﬂuences the equation as well as the boundary condition" (Accepted 2019).

Ananta Acharya

Ph.D. in computational mathematics, graduated 2023, UNCG.
Manuscript titled "Analysis of reaction-diffusion systems where a parameter influences both the reaction terms as well as the boundary" (Accepted in 2020).
Manuscript titled "Sigma-shaped bifurcation curves" (Accepted in 2021).

Dustin Nichols

Current Ph.D. in computational mathematics, graduated 2023, UNCG.
Manuscript titled "Modeling effects of matrix heterogeneity on population persistence at the patch-level" (Accepted in 2022).

Keta Henderson

Current Ph.D. in computational mathematics, graduated 2023, UNCG.
Manuscript titled "Modeling effects of matrix heterogeneity on population persistence at the patch-level" (Accepted in 2022).

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