SPS 5088 Graduate General Relativity final project at the Florida Institute of Technology. Derives global AdS₄ from the vacuum Einstein equations, builds the Laplace–Beltrami operator and flat-space limit, reduces the Klein–Gordon equation to a radial ODE, studies conformal-boundary asymptotics and the Breitenlohner–Freedman bound, and compares global versus Poincaré patch charts. Further work in progress on boundary-condition-dependent dynamics and numerical radial solutions.

Extra credit project for PHY 4030 Subatomic Physics at the Florida Institute of Technology, Spring 2026.
Results were inconclusive. The writeup documents construction and failure modes.

Slides for MTH 4105 Topology midterm, Spring 2026, at the Florida Institute of Technology. Introduced fiber bundles, vector bundles, principal bundles, connections and curvature, finishing with how U(1) gauge theory recovers Maxwell’s equations in vacuum.

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Journal club slides on Mark van Raamsdonk’s 2010 paper: entanglement builds bulk geometry via AdS/CFT and the Ryu–Takayanagi formula, with a thread to ER=EPR. Presented at SPS Journal Club, Florida Institute of Technology, Spring 2026.

Abstract Algebra presentation on orthogonal and unitary groups and their role as rotations in physics, given at the Florida Institute of Technology in December 2025. Expanded lecture notes on “What is Spin?” and related material.

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Presentation on the Einstein–Podolsky–Rosen paradox and the completeness of quantum mechanics, given at SPS Journal Club, Florida Institute of Technology.

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Exploring quantum entanglement fundamentals through the Clauser-Horne-Shimony-Holt (CHSH) inequality, investigating quantum vs. classical correlations, derivation of the Tsierelson bound.

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Introductory LaTeX workshop for the Society of Physics Students (SPS), jointly organized by the Department of Mathematics and the Department of Physics and Space Sciences, Florida Institute of Technology, and directed at incoming freshmen. In collaboration with Overleaf

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