9 topics · 52 articles
Study
Things I'm studying, for research or for myself.
Physics Engines
How physics engines actually work on the inside, from the core math to contact optimization, XPBD, and GPU-scale simulation.
Linear Algebra
The language underneath everything else. Linear maps, worked from vectors and elimination up to eigenvalues, the SVD, and numerical conditioning.
Convex Optimization
The optimization that runs inside contact solvers and policy updates, covering convex sets, quadratic programs, duality, cones, and how solvers descend.
Optimal Control
Computing controls for the systems a physics engine simulates, from LQR and dynamic programming to iLQR and MPC, with the Bellman bridge to reinforcement learning.
Probability & Information Theory
The probability behind RL and state estimation. Expectation and Monte Carlo, entropy and KL divergence, the score-function gradient, and Bayesian filtering.
Lie Groups & Manifolds
The geometry of rotation and motion, done properly, with SO(3)/SE(3), the exponential map, and optimization on curved spaces for orientation and pose estimation.
Reinforcement Learning Theory
The math spine of RL. MDPs and value functions, the Bellman operators, policy gradients, and the trust-region and natural-gradient methods that stabilize them.
Matrix Calculus & Autodiff
How gradients actually get computed for learning and differentiable simulation, through matrix calculus, forward vs reverse-mode AD, backprop, and differentiating a physics step.
The Jacobian Conjecture
An 85-year-old problem about when a polynomial map must be invertible, and the July 2026 map in C^3 that appears to break it: locally invertible everywhere, yet many-to-one globally.