Conducted research under a University of Pennsylvania PhD candidate on discrete mathematics and Ramsey theory.
Investigated Ramsey numbers, the Hales-Jewett theorem, Van der Waerden's theorem, and the Lovász Local Lemma.
Authored a paper utilizing the Lovász Local Lemma to prove existence of structures in probabilistic combinatorics, deducing Van der Waerden's Theorem via Hales-Jewett.
Jun 2025 — Aug 2025
Whole Foods Market
Cashier
Delivered efficient checkout service handling cash, credit, and digital transactions via POS systems.
Collaborated with team members on restocking and front-end operations during high-traffic hours.
A comprehensive guide covering graph theory, combinatorial proofs, counting principles, and discrete structures — written for students bridging undergraduate math and theoretical CS.
30 essential integrals for higher mathematics with original step-by-step solutions. Designed to strengthen understanding of key integral techniques for advanced math learners.
Abstract
A graph G on n vertices is maximal k-colorable if χ(G) = k and adding any edge raises the chromatic number — equivalently, G is a complete k-partite graph. This paper studies the edge spectrum Σχ(n, k): the set of all edge counts realized by such graphs. We prove the saturation number satχ(n, k) = (k−1)(2n−k)/2 and the abundance abχ(n, k) = ex(n, Kk+1). We show Σχ(n, k) is a complete integer interval if and only if n ≤ k + 2, determine Σχ(n, 2) exactly with explicit gap formulas, and give a parametric description for k = 3 including identification of the first partition collision at n = 9. We also establish the strict containment Σχ(n, k) ⊊ ES(n, Kk+1) for n ≥ k + 3.
Chromatic SaturationComplete Multipartite GraphsEdge SpectrumTurán GraphExtremal Graph TheoryPartition Theory
Led 200+ members, coordinating peer tutoring programs and community service initiatives.
Organized monthly meetings, developed tutoring schedules, and facilitated communication between students and faculty.
Managed leadership projects focused on academic excellence and community engagement.
Fitness & Partnerships
Beyond the Screen
Transparent Labs
Brand Partner & Affiliate
I partner with Transparent Labs — one of the most science-backed supplement brands in the industry — as a fitness content creator and affiliate. I create fitness content focused on training, nutrition, and performance, and share evidence-based supplement recommendations with my audience.