I began my research career as soon as I entered university, despite having limited mathematical background at the time. I focused on the Homotopy Analysis Method (HAM), a powerful technique for finding numerical solutions to ordinary and partial differential equations. By the end of my second year, I had published my first abstract at the ICCME 2023 conference, where I presented several numerical examples based on physical scenarios to demonstrate the effectiveness of the method.
My undergraduate research focuses on Infinite-Dimensional Topology and Large-Scale Geometry. Z-sets, as subsets of the Hilbert cube, are a central concept in infinite-dimensional topology. In this study, we extend the notion of Z-sets from infinite-dimensional topology to large-scale geometry, introducing the concept of Coarse Z-sets. This result contributes to combining ideas between these two areas. I presented this work as an abstract at the ICCME 2025 and RESCON 2025 conferences.
Z-set in Large Scale Geometry Thesis PDF
Z-SETS IN LARGE SCALE GEOMETRY (ICCME 2025 Accepted)
COARSE Z-SET INVARIANCE UNDER COARSE EMBEDDINGS (RESCON 2025 Submitted)
Engaging in a collaborative research project related to the Duistermaat-Heckman theorem,combined with Fourier transformation, quantum mechanics, and functional analysis.
I go by Akalanka Chandralal, or Akalanka.
Email akalankad at sci dot pdn dot ac dot lk