Research
Preprints and Publications
Improved Weyl bounds on short intervals (2026). arXiv:2609.02478.
Complexity-sensitive additive energy and off-diagonal Young inequalities on bounded-degree algebraic varieties (2026). arXiv:2608.18956.
Lonely Runners over Function Fields: Quantized Phase--Riesz product (2026). arXiv:2608.18818.
Factorial residues modulo a prime: beyond the square-root bound (2026). arXiv:2608.01781.
Sharp Hausdorff Bounds for the Interior Singular Set of Convex k-Hessian Solutions (2026). arXiv:2607.28988.
Phase-randomised Riesz products and a further improvement towards the lonely runner conjecture (online note with Benjamin Bedert, 2026; both authors independently obtained the exponent 13/8, each with AI assistance; the proof presented in the note was developed primarily by AI). PDF.
Exploratory Research Notes
These notes record exploratory results and intermediate steps from ongoing investigations. Some observations may already be known, while others establish only one part of a broader argument rather than a complete proof.
Separating Prime Blocks and Phase-Resolved Asymptotics for Harmonic Subset Sums.
Reflection Completions and Weighted Stability for Strongly 2-Primitive Sets.
A Gibbs-Greedy N2/3 Construction for Sine Sums and Riesz-Product Consequences of Two-Dissociation.
A logarithmic-square construction for squarefree pairwise sums.
From Isospectrality to Geometry.
Notes on Erdos Problem 143: GCD Graphs, LYM Flows, and Multiscale Packing.