Alejandro José Soto Franco

I was trained as a biomedical engineer at Johns Hopkins University, where research on active matter physics and fluid mechanics pulled me into differential geometry and PDE theory as the right languages for physical systems. The same Riemannian geometric framework that describes defect dynamics in curved active nematic substrates applied to price dynamics on non-stationary diffusion manifolds. That connection shapes everything I build.

My research sits at the boundary of geometric analysis, fluid mechanics, and active matter physics. The active nematics work I did at Hopkins produced a co-authored paper submitted to Proceedings of the National Academy of Sciences (arXiv:2503.10880), showing that +1/2 topological defects in confined two-dimensional active nematics generically lock into periodic orbits (golden and silver braids) whose periodicity is governed by metallic ratios and whose chaotic mixing properties are captured by the Burau representation of braid groups.

I previously worked as a Rust trading strategies developer at Anti Capital in New York, where I shipped a pre-debit balance guard that eliminated insufficient-balance order rejections across a multi-exchange market-making execution stack.

I now lead Holonomy Securities as Founding Principal, where a three-person team builds systematic trading engines across prediction markets and equity options on a shared platform substrate. That substrate, Colosseum, is a multi-asset quantitative backtesting and execution platform with a WASM strategy sandbox, CLOB-native data, configurable fill models, and full audit trail, built on a Rust engine with an axum API and a Next.js frontend; we launched it this month. Our primary engine on top of Colosseum is Polybius, a Polymarket-native binary options system with non-stationary SDE regime models and CLOB execution; it has returned roughly 81% since going live. Alongside Polybius we are building three further engines: Malliavin (regime-conditional QQQ options with directional spreads and vol selling), Bismut (volatility surface curvature signals from SSVI-fit Riemannian geometry), and Hsu (manifold-valued realized covariance on SPD(N) with affine-invariant metrics).

In parallel I maintain open-source Rust libraries for geometric computing and stochastic analysis, published on crates.io and PyPI: cartan (Riemannian geometry, Lie-group optimisation, and stochastic processes on manifolds), pathwise (non-Markovian SDE simulation with manifold-valued state), volterra (covariant active nematics on simplicial meshes), and elworthy (a JIT compiler that specialises Bismut-Elworthy-Li formulas into SIMD kernels for unbiased Monte Carlo Greeks on non-stationary SDEs).

Through mermin, my Rust toolkit for k-atic alignment analysis of fluorescence microscopy, I collaborate with the University of Pittsburgh School of Medicine on studies of human vaginal fibroblasts: Minkowski tensor shape descriptors, multiscale structure tensors, persistent homology, and SO(3) holonomy-based topological defect detection applied to the orientational order of cell monolayers.

In April 2026 I landed my first contribution to Mathlib4 (PR #38022): closure lemmas showing that functions with compact multiplicative support form a submonoid, with follow-on results for List, Multiset, and Finset products.

Outside of work: I cook, DJ, lift, and play Supreme Commander: Forged Alliance.