Projects

Cartan

Riemannian geometry on smooth manifolds. Connection forms, parallel transport, holonomy groups, and geodesic flows. Documentation at cartan.sotofranco.dev.

Volterra

Covariant active nematics solver built on Cartan. Dimensionally agnostic: any type implementing cartan_core::Manifold serves as the simulation domain. Beris-Edwards equations on arbitrary Riemannian geometries via discrete exterior calculus.

von Karman

Multi-precision pseudospectral Navier-Stokes solver. ETD-RK4 time integration with Kassam-Trefethen contour integral, dealiased 3/2 cross product, adaptive CFL. Five initial conditions, energy spectrum diagnostics, HDF5 snapshots, Parquet time series.

Elworthy

JIT compiler that specialises Bismut-Elworthy-Li formulas into SIMD kernels for unbiased Monte Carlo Greeks on non-stationary SDEs. Symbolic AST, Cranelift lowering (scalar and 2-lane F64X2), multi-dimensional Heston driver, pathwise and likelihood-ratio Malliavin parameter Greeks (machine-checked with SymPy). European call price and BEL delta cross-validated against Black-Scholes closed form and the independent blackscholes crate; both agree within four Monte Carlo standard errors. About 22x over a tree-walking interpreter on GBM paths.

Kloeden

Hand-written SIMD C++ vs Rust (LLVM + Cranelift) benchmark companion to pathwise and elworthy. Same Brownian-increment fixture across four impls; single-thread pinned-core throughput on scalar Euler / Milstein / Taylor 1.5 on GBM, plus a digital-delta correctness table showing naive pathwise silently returns 0 in both languages while the Bismut-Elworthy-Li constant-flow weight matches analytic within 4 Monte Carlo standard errors (bitwise-identical between hand-rolled C++, hand-rolled Rust, and elworthy_rt::from_paths). Named after Peter Kloeden.

Mermin

k-atic alignment analysis of fluorescence microscopy. Minkowski tensor shape descriptors, multiscale structure tensor fields, topological defect detection via cartan-geo SO(3) holonomy, persistent homology, spatial statistics, and Landau-de Gennes parameter fitting. Outputs calibrated parameters for forward simulation in volterra. 7 crates on crates.io, Python bindings on PyPI.

Polybius

Live Polymarket prediction market engine. BTC/ETH WebSocket price feed drives a 5-minute directional and regime model; orders execute on the Polymarket CLOB via a custom Rust signing layer.

Malliavin

Options volatility surface engine. Multi-agent regime detection, coarse-grained signal emission, vol surface manifold. Deployment target: Deribit and IBKR.

Bismut

Volatility surface manifold toolkit. Malliavin calculus-based Greeks, SDE vol models, and backtest infrastructure for equity derivatives.

inferCNAsc

Copy number variation and ascertainment bias inference for single-cell genomics. Rust compute core with Python bindings via PyO3/maturin. Published on PyPI.

Gas Leak Rate Calculator

Subsurface safety valve gas leak rate calculator per API RP 14B 5th edition. Dranchuk-Abou-Kassem equation of state. Free, unlimited calculations.