Peer-reviewed · Open access
Independent mathematical work — preprints and expository papers written independently while studying A-level Mathematics and Further Mathematics.
Read, cite, and download the preprints and journals shaping modern theory — from spectral geometry to the Navier–Stokes equations, curated and cross-referenced.
We establish a priori estimates guaranteeing smoothness of weak solutions to the three-dimensional Navier–Stokes system on finite time intervals, extending the Ladyzhenskaya framework to time-dependent external forcing.
Greedy constructions, recurrences, and emergent arithmetic structure.
Networks, spectra, and walks over vertices and edges.
Continuity, homotopy, and the shape of space itself.
Primes, modular forms, and arithmetic structure.
Stochastic processes and measure-theoretic limits.
Curvature, geodesics, and Riemannian structure.
Limits, convergence, and functional spaces.
Set theory, models, and the limits of proof.
Paper of the week
We construct a self-adjoint operator whose eigenvalues coincide with the nontrivial zeros of the Riemann zeta function, yielding a conditional path to the long-standing conjecture via spectral theory.
Read the paperA bridge between differential forms and the cohomology of projective varieties: we verify the Hodge conjecture for a new class of abelian fourfolds with prescribed endomorphism structure.
New asymptotic bounds on stopping times for the 3x+1 iteration, obtained via a stochastic model refined with recent lower bounds on nontrivial cycles.
Spectral distributions for large non-Hermitian ensembles under multiplicative noise; we prove almost-sure convergence to the circular law and quantify the rate of convergence.