webglfan

  1. **Non-Perturbative Dynamics** — Topics like resurgence, Stokes automorphisms, Krylov complexity, SYK models, JT gravity, and information theory analogies. ([Gist][1])
  2. **Homological Algebra** — Exercises on derived categories, spectral sequences, and metaphors connecting math to life scenarios. ([Gist][1])
  3. **Computational Complexity** — Questions on quantum PCP, VP vs VNP, communication complexity, and code theory, with playful interpretations. ([Gist][1])
  4. **Topological Field Theory** — TQFT axioms, cobordism hypothesis, Reshetikhin-Turaev invariants, and analogies like “gossip as factorization algebra.” ([Gist][1])
  5. **Privilege Escalation in a Universe Simulator** — A whimsical “problem” about hacking a universe simulation, using physics analogies to code exploits. ([Gist][1])

    \[
    P(z) = \sum_{k=0}^{100} c_k z^k
    \]

    where the coefficients \( c_k \) are defined as:

    \[
    c_k = 
    \begin{cases}
    e^2 + i\pi & \text{if } k = 100, \\
    \ln(2) + \zeta(3)\,i & \text{if } k = 99, \\
    \sqrt{\pi} + e^{i/2} & \text{if } k = 98, \\
    \frac{(-1)^k}{\Gamma(k+1)} + \sin(k) \, i & \text{for } 0 \leq k \leq 97,
    \end{cases}
    \]