Brownian motion on a deforming manifold

Kuramoto model on $S^2$

Hopf fibration $S^3 \to S^2$

Interstellar: a brane-bulk reading ◆Chaos-generating periodic orbits of topological defects in confined active nematics From RVE to Mesh: A Pipeline for Heterogeneous Continua ◆On the Regularity of Three-Dimensional Navier-Stokes Solutions: A Geometric Approach via the Biot–Savart Connection Analysis on Manifolds V: Stokes’ Theorem Analysis on Manifolds IV: Integration Analysis on Manifolds III: Differential Forms Analysis on Manifolds II: Exterior Algebra Probability and Statistics: A Geometric Foundation Numerical Analysis via Discrete Exterior Calculus Accounting in Quantitative Finance and Algorithmic Trading Analysis on Manifolds I: Analysis on ℝⁿ Performance Measurement Under Uncertainty The Kelly Criterion from Shannon Information Theory Reservoir Geometry: Riemannian Manifolds in Oil and Gas Rust, from first principles Maxwell's Equations and Gauge Theory: Electromagnetism as a Principal Bundle Navier–Stokes: Derivation in ℝ³ and on a Riemannian Manifold Price as Geometry: Resolution, Coarse-Graining, and the Structure of Market Noise Diffusion on Curved Spaces Manifolds: The Language of Modern Geometry Kuramoto: How Order Emerges from Chaos BTC/ETH Lead-Lag: Resolution-Dependent Direction Reversal on Binance Spot

Interstellar: a brane-bulk reading ◆Chaos-generating periodic orbits of topological defects in confined active nematics From RVE to Mesh: A Pipeline for Heterogeneous Continua ◆On the Regularity of Three-Dimensional Navier-Stokes Solutions: A Geometric Approach via the Biot–Savart Connection Analysis on Manifolds V: Stokes’ Theorem Analysis on Manifolds IV: Integration Analysis on Manifolds III: Differential Forms Analysis on Manifolds II: Exterior Algebra Probability and Statistics: A Geometric Foundation Numerical Analysis via Discrete Exterior Calculus Accounting in Quantitative Finance and Algorithmic Trading Analysis on Manifolds I: Analysis on ℝⁿ Performance Measurement Under Uncertainty The Kelly Criterion from Shannon Information Theory Reservoir Geometry: Riemannian Manifolds in Oil and Gas Rust, from first principles Maxwell's Equations and Gauge Theory: Electromagnetism as a Principal Bundle Navier–Stokes: Derivation in ℝ³ and on a Riemannian Manifold Price as Geometry: Resolution, Coarse-Graining, and the Structure of Market Noise Diffusion on Curved Spaces Manifolds: The Language of Modern Geometry Kuramoto: How Order Emerges from Chaos BTC/ETH Lead-Lag: Resolution-Dependent Direction Reversal on Binance Spot

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Alejandro Soto Franco

MathematicianRust EngineerQuant

Working at the intersection of PDE theory, geometric analysis, and high-performance quantitative systems. Research spans fluid mechanics, active matter physics, and non-stationary stochastic models of financial markets.

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