Writing & projects

Exposition

A collection of mathematical exposition, presentations, and miscellaneous projects written over the years.

Mathematics in Everyday Life

Cool ways in which mathematics appears in everyday life, written for a general audience.

A sound wave followed by progressively smaller delayed echoes

Fourier analysis · Interactive notebook What Are Echoes? Explore how echoes form and why the same sound can feel different in different spaces—then upload a WAV file and hear how it changes across several virtual venues. Launch interactive notebook Binder may take a minute to start.

Graduate Exposition

Technical expositions and research-driven writing from my graduate studies, intended for readers with a stronger mathematical background.

Supporting lines tangent to a convex set, with marked contact points and outward normals

Convex analysis · PDF Duality in Mathematics An introduction to the recurring idea of duality through complements, cones, vector spaces, planar graphs, population genetics, convex conjugates, and Lagrangian optimization. Read the exposition

Abstract illustration of a smooth interpolating surface passing through control points

Applied mathematics · PDF Extensions of Thin Plate Splines Univariate splines arise naturally from a roughness-penalty approach to nonparametric regression. This note extends these ideas to higher dimensions, where there is no natural polynomial analogue. Read the exposition

Illustration of a symmetry-maximizing fair-value mechanism

Mathematical finance · PDF Symmetry-Maximizing Fair Values A symmetry-based method for extracting fair-value information from limit-order-book depth. Read the exposition

Phylogenetic tree topologies arranged around connected geometric cells in BHV tree space

Phylogenetics · PDF Brownian Motion in BHV Tree Space An introduction to the geometry of Billera–Holmes–Vogtmann tree space and the construction of Brownian motion, bridges, and Bayesian inference for distributions of phylogenetic trees. Read the exposition