Math & physics work

Cl(3,0) geometric-algebra encoding + tree tensor network circuit

Encodes gravitational-wave polarizations (h+, h×) as a Cl(3,0) multivector, with the phase residual carried as the Hodge-dual third component, then classifies echo / no-echo ringdown signatures — a quantum-gravity proxy — with a Spin(3)-equivariant tree tensor network circuit. Targeting IBM ibm_kingston hardware.

Multi-domain scientific foundation model, swarm-of-primitives architecture

A physics-constrained foundation model spanning gravitational-wave, condensed matter, and materials domains. Replaces mixture-of-experts routing with six composable mathematical primitives — conserved-current, response/Green's function, extremal/variational, spectral/eigenstructure, group-equivariant, and renormalization — that assemble into domain experts. Phase-1 falsification target: GW quasinormal-mode pole recovery and cascade damage scaling. Built in collaboration with Michael Lawler (Cornell/Binghamton).

PINN-constrained PPO control agent for BOUT++ plasma simulation

A reinforcement-learning control agent (PPO) constrained by a physics-informed neural network, with Clifford geometric-algebra layers and a chalcogenide memristor reservoir computing backend, controlling BOUT++ plasma simulations in real time. Source published on GitHub; PyPI packaging in progress.

Positive-geometry approach to scattering amplitude computation

A solver built around the amplituhedron formalism, computing scattering amplitudes from positive-geometry structure directly rather than summing Feynman diagrams. Shares a throughline with the Clifford/geometric-algebra work: physics encoded as geometric structure rather than as a sum over terms.

Interactive explorer for hyperbolic and spherical geometry

An interactive visualization tool for building intuition in hyperbolic and spherical geometry — tessellations, geodesics, and curvature made explorable rather than only equational.

Agent architectures with geometric-algebra state representations

Exploratory work on agent architectures that carry state as geometric-algebra multivectors rather than flat vectors, extending the same Clifford-algebra approach used in the GW classifier and plasma control agent into general agent design.

Fast learned surrogates for expensive physics simulations

Learned surrogate models standing in for expensive numerical solvers (field simulations, plasma dynamics) — trading a controlled amount of accuracy for orders-of-magnitude speedup, with error bounds tracked explicitly rather than ignored.

Physics-constrained CAD for magnet and coil design

JAX-based Biot–Savart field solver with optax-driven geometry optimization for designing coils and magnet assemblies against physical field constraints, not just geometric ones.