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Broad Area: Fractal Geometry.
Previous Work/Experiences:
Formulating an iterated function system (IFS) on the sphere (Euclidean space) consists of
transformations constructed using the Stereographic projection map and its inverse map.
Providing detailed constructions of an affine fractal interpolation function (FIF) on the real projective
plane (non-Euclidean space).
Estimating the fractal dimension of the graph associated with a FIF on the real projective plane.
Providing constructions of a non-affine FIF on the real projective plane and also developing the idea of
constructions of non-affine FIF on the dual of the real projective plane.
Initiating the quantization theory for Cantor-like set on the real projective line.
Core Research Interests: My primary research interest revolves around estimating the fractal dimensions
of diverse fractal sets and exploring the dimensional characteristics of invariant probability measures
associated with fractals and Computer vision. Additionally, I am keenly interested in developing the theory of fractal interpolation
in Euclidean as well as non-Euclidean spaces and its applications to approximations.
Closing Statement: In summary, my research interests lie in fractal geometry and related topics, aiming to
contribute novel insights. Through interdisciplinary collaboration, I seek to address pressing questions and
make meaningful contributions to society. With dedication and curiosity, I strive to push the boundaries of
understanding in my chosen field.
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