PRINCESS PEARL AMANIE

Applied mathematician with a recently completed Master's degree in Mathematical Sciences from the African Institute for Mathematical Sciences (AIMS), Ghana, and a Bachelor's degree in Mathematics and Statistics from the University of Ghana. My research interests lie in partial differential equations, functional analysis, operator semigroup theory, and numerical analysis. My master's research focused on the spectral growth and stability of $C_0$-semigroups arising from abstract Cauchy problems, while my undergraduate research was on the Virtual Element Methods for the Poisson equation. I am seeking doctoral research in nonlinear PDEs, functional analysis, and related areas of mathematical analysis. Hardworking and proactive individual, dedicated to providing exceptional learning experiences for students. Experienced in performing class administrative activities accurately and preparing engaging learning materials and lesson plans. Friendly and open communicator with excellent time management skills.

• Mastercard Foundation Scholar, AIMS Ghana (2025–2026)
• Ernst & Young Undergraduate Scholarship Recipient (2022–2024)
• Certificate in Business Analytics and Data Visualisation (2024)
• Certificate of Completion – Girls in Mathematical Sciences Program, AIMS Ghana (2021)

• Joseph, Owino, Dr., jowino@aims.edu.gh, African Institute for Mathematical Sciences (AIMS), Ghana, Research Tutor for Master’s Thesis
• Vincent, Teyekpiti, Dr., vteyekpiti@ug.edu.gh, University of Ghana, Lecturer and Undergraduate Thesis Supervisor

Spectral Growth and Stability Analysis of C₀-Semigroups and Abstract Cauchy Problems | 2026

• Investigated the spectral properties of linear operators generating strongly continuous (C₀) semigroups.
• Studied the well-posedness and asymptotic stability of abstract evolution equations using functional analysis.
• Applied semigroup theory, operator theory, and spectral analysis to linear partial differential equations.
• Strengthened mathematical analysis and independent research skills through theoretical investigation.

Maximum Principles for Second-Order Elliptic Equations | 2025

• Studied weak and strong maximum principles for second-order elliptic equations.
• Investigated Hopf's boundary point lemma and uniqueness results for elliptic partial differential equations.
• Developed a strong foundation in the qualitative analysis of elliptic PDEs.

The Virtual Element Method for the Poisson Equation | 2024

• Developed MATLAB implementations of the lowest-order Virtual Element Method for solving elliptic boundary value problems.
• Derived weak formulations and implemented numerical discretisations on polygonal meshes.
• Conducted convergence studies and compared numerical results with classical finite element methods.
• Enhanced computational mathematics and scientific programming skills using MATLAB.

• Master’s Thesis Defence: Spectral Growth and Stability Analysis of C0-Semigroups and Abstract Cauchy Problems, African Institute for Mathematical Sciences (2026).
• Seminar Presentation: Maximum Principles for Second-Order Elliptic Equations, African Institute for Mathematical Sciences (2025).
• Undergraduate Research Presentation: The Virtual Element Method for the Poisson Equation, University of Ghana (2024).

• Nonlinear Partial Differential Equations and Functional Analysis
• Operator Semigroup Theory and Spectral Theory
• Geometric and Variational Analysis
• Numerical Analysis and Mathematical Modelling

• Partial Differential Equations and Functional Analysis
• Real and Complex Analysis
• Measure Theory and Probability Theory
• Numerical Analysis, Scientific Computing, and Mathematical Modelling

• Student Financial Representative, African Institute for Mathematical Sciences (AIMS), Ghana (2025–Present)
• Public Relations Officer and Event Coordinator, Department of Mathematics, University of Ghana (2023–2024)
• Finance Committee Member, Department of Mathematics, University of Ghana (2021–2022)