Om Shah · San José, California

Applied mathematics,
built like working software.

Applied Mathematics student at SJSU, undergraduate researcher in geometric topology, and a robotics hacker who ships autonomous systems. I care about proofs that hold and code that deploys.

om@sjsu - zsh

Academic

Research

B.S. Computational & Applied Mathematics

San José State University · transferred from Moorpark College

SJSU

Student Assistant - Geometric Topology

At the San José State University Research Foundation, working with Assistant Professor Edgar A. Bering IV on a novel generalization of Theorem 5.1 of Coloring the Curve Graph (Gaster, Greene, Vlamis, 2016) from the curve graph of a surface to the sphere graph of a connected sum of copies of $S^{1} \times S^{2}$ .

SJSURF

The result, in the language of the problem

The curve graph $C (S)$ admits a proper coloring whose chromatic number is controlled by the topological complexity of the surface. We ask the analogous question for the sphere graph $S (M_{n})$ of the manifold $M_{n} = #_{n} (S^{1} \times S^{2})$ :

χ (S (M_{n})) \leq 3 n - 4, n \geq 3.

The bound is realized by a coloring built from the geometric intersection number, mirroring the surface case where Gaster, Greene, and Vlamis establish

χ (C (S_{g})) = Θ (\frac{g ^{2}}{lo g g}) .

Here $S_{g}$ is the closed orientable surface of genus $g$ , and $#$ denotes connected sum.

Projects & Tech

What I build

Two threads, one habit: take a hard system, find the right abstraction, and make it dependable. Switch between them below.

Athyna

Omm2005/Athyna

An open-source AI research companion that helps you collect, organize, and interrogate papers - keeping the reading loop tight so the thinking stays the hard part. Built with a typed, end-to-end stack and a schema-first data layer.

Next.js
TypeScript
Tailwind
Supabase
Drizzle ORM

Type safety: end-to-end
Data layer: schema-first
License: open source

How I work

Engineering practices

CI/CD by default

Every change runs through automated build, test, and lint gates before it merges. Green pipeline or it does not ship.

Measured, not guessed

Decisions follow metrics - the 150% robotics accuracy gain came from instrumenting the loop and tuning against the numbers.

Accessible & predictable

Keyboard-first navigation, visible focus, semantic structure, and layouts that behave the same on every screen.

Typed end to end

Strong types and schema-first data from the database to the UI, so refactors are safe and the compiler catches the rest.

0%accuracy gain

0tests passing

100%typed surface

Off the clock

Outside the proofs

Primary inspiration

Queen, on repeat

'Bohemian Rhapsody' is the closest thing I have to a north star - six minutes that change key four times and still resolve. Ambition with structure.

Hi-fi audio

High-fidelity listening

Lossless tracks, a quiet room, and good gear. Hearing the detail in a mix is its own kind of close reading.

5-day split

Gymmaxxing

A five-day split, run with the same discipline as a proof - progressive, measured, and consistent over flashy.

SoCal by transit

Riding the rails

Exploring Southern California by public transit and train. Slower than driving, better for watching a system actually move people.

Get in touch

Contact

Open to research collaborations and hard engineering problems. The code lives on GitHub - the fastest way to see how I work is to read it.

GitHubOmm2005

$□$ Built with proofs in mind.