Projects

Extremal values of Grönwall’s ratio $\sigma (n)/(n\log \log n)$ for $n\ge 5041$ with a fixed number of distinct prime factors, the gap between integer and real-exponent optima, and bounds for counterexamples to Robin’s inequality.

Sharper error bounds for the normal approximation of sums of independent, not necessarily identically distributed, random variables.

An engine for Scrabble-like games on boards assembled from finite path and cycle word tracks, with configurable scoring rules, handicaps and buffs, and many other extensions and variations.

An investigation of formulation search for closed first-order formulas over the reals whose atomic relations are quadratic.

Compute rigorous upper and lower bounds for the operator norm in Trefethen’s third hundred-digit challenge problem: the norm of the infinite matrix formed by arranging $1,1/2,1/3,\dots$ along successive antidiagonals.

A lightweight asynchronous system for multi-objective black-box and hyperparameter optimization, with a Rust engine, Python interface, and a common ask-and-tell protocol for local or distributed studies.

Worst-case guarantees for gradient descent with steps fixed in advance, and their dependence on the number of steps, dimension, and whether negative steps are allowed.

A distributed method for coordinating the trades of multiple portfolio managers so that a firm can reduce transaction costs while preserving the separation of their individual optimization problems.

An efficient method and open-source implementation for attributing the out-of-sample performance of a least-squares regression model to its input features using Shapley values.

A 2021 Stanford Undergraduate Research Institute in Mathematics project on direct and combinatorial proofs of Tokuyama’s formula and possible routes toward analogues for symplectic groups.