Symplectic Geometry & Classical Mechanics In Progress...|
Project_
Riemannian Geometry In Progress...|
Notes_
Ideas of Algebra | Ideas of Analysis | Ideas of Geometry In Progress...|
$$\huge TM\oplus T^*M$$
Exposition X Sci. Com X Teaching_
Ideas of Quantum Field Theory In Progress...|
Exposition X Sci. Com X Teaching_
Gauge Field Geometry. In progress...|
Semester & Summer Project_
An exposition presenting the geometric foundations of gauge theory and relate them to the physical theories of electromagnetism, Yang-Mills, and gneral relativity. We also outline their influence on low-dimensional topology, particularly through their connections to Knot theory and four-manifold invariants.
Differential Geometry.
Lecture Notes_
Lecture notes on manifolds, tangent spaces, submanifolds, vector bundles, vector fields, differential forms, integration on manifolds and Stokes' theorem.
AdS/CFT Correspondence.
Master's Thesis_
Studied Riemannian geometry, AdS geometry, structure of 2d CFTs, and their connections.Computed boundary CFT correlation functions via bulk AdS gravity using two equivalent AdS/CFT prescriptions. Related Fefferman & Graham conformal invariants (the ambient metric framework) to some formal aspects of conformal boundary in AdS/CFT.
Energy Transfer in Electric Circuits.
Semester Project_
Built a 39m long transmission-line model to demonstrate the artefacts of a field-based (Poynting vector) energy transfer. Recorded nanosecond level voltage steps (40-140ns) across the load using a GHz oscilloscope.
Finite Difference Methods.
Semester Project_
Implemented finite difference methods for PDEs, including the schemes of Gauss-Seidel, SOR, andMultigrid to improve convergence. Demonstrated these methods on a Laplace equation with specified boundary constraints.