Hello World: Building This Site

Welcome to my personal site. This is the first post, and it doubles as a tour of the technical stack behind it.

The Stack

This site is built with:

Next.js (App Router) — a React framework for building fast, modern websites
TypeScript — typed JavaScript that catches bugs before runtime
Tailwind CSS — utility-first CSS for rapid styling
MDX — Markdown with embedded React components
KaTeX — LaTeX math rendering
Shiki — syntax highlighting for code blocks

Everything is statically exported and deployed on GitHub Pages — no server required.

Markdown Features

Code Blocks

Here's a Python snippet with syntax highlighting:

import numpy as np
 
def solve_ode(f, y0, t_span, dt=0.01):
    """Simple Euler method for ODE integration."""
    t = np.arange(t_span[0], t_span[1], dt)
    y = np.zeros((len(t), len(y0)))
    y[0] = y0
    for i in range(1, len(t)):
        y[i] = y[i-1] + dt * f(t[i-1], y[i-1])
    return t, y

Inline Math

Einstein's mass-energy equivalence: $E = mc^2$ .

The Euler identity: $e^{i\pi} + 1 = 0$ .

Block Math

The Navier-Stokes equations for incompressible flow:

\frac{\partial \mathbf{u}}{\partial t} + (\mathbf{u} \cdot \nabla)\mathbf{u} = -\frac{1}{\rho}\nabla p + \nu \nabla^2 \mathbf{u} + \mathbf{f}

\nabla \cdot \mathbf{u} = 0

Lists and Formatting

Some things I'm excited to write about:

Neural operators — learning PDE solution mappings
Diffusion models — generative approaches to scientific computing
Mathematical foundations — approximation theory, spectral methods

"The purpose of computing is insight, not numbers." — Richard Hamming

What's Next

I'll be posting technical deep-dives on my research, notes on interesting papers, and occasional personal reflections. Stay tuned.