Patrick Erik Bradley

activity

20242026

collaborators

10 papers

math.AG2026

Searching Schemes With $p$ -Adic Neumann Boundary Value Problems

Patrick Erik Bradley

Firstly, for branched covering maps $f : Y \to X$ between smooth, separated schemes of finite type over the integral ring $O_{K}$ of a non-archimedean local field $K$ , the ramific…

math.NT2026

Hearing Tamagawa Factors modulo $q - 1$

Patrick Erik Bradley

The Tamagawa factor w.r.t.\ the prime $p$ of an abelian variety $A$ over a non- archimedean local field $K$ is found to be congruent modulo $q - 1$ to the wavelet eigenvalues of a…

math.PR2026

$p$ -Adic Diffusion and Random Walks on $[0, 1]$

Patrick Erik Bradley, Paulina Halwas, Ell Ari Nitsche +1

Integral operators on the real unit interval are constructed as transported from ones on the $p$ -adic unit disc via the Monna map. This gives rise to strong Markov processes on $[0…

math.AP2026

Neumann Boundary Value Problems on $p$ -Adic Analytic Manifolds

Patrick Erik Bradley

Inspired by graph theory, Neumann Boundary Value Problems on $p$ -adic analytic manifold are formulated. Existence and uniqueness of weak solutions is proven in the ultracontractive…

math.NT2026

Boundary Value Problems on $p$ -Adic Analytic Manifolds

Patrick Erik Bradley

An account is given on newest developments on $p$ -adic boundary value problems on $p$ -adic analytic manifolds and their relationship with diffusion. In particular, novel coordinate…

math.NT2025

Hearing the Serre invariant of a compact $p$ -adic analytic manifold

Patrick Erik Bradley, Ángel Morán Ledezma

Using a previous novel way of defining kernel functions for Laplacian integral operators on a compact $p$ -adic analytic manifold $X$ , one such operator $Δ_{0}^{s}$ with $s\in\mathds{R}…

math.AP2025

Boundary Value Problems for p-Adic Elliptic Parisi-Zúñiga Diffusion

Patrick Erik Bradley

Elliptic integral-differential operators resembling the classical elliptic partial differential equations are defined over a compact d-dimensional p-adic domain together with assoc…

math.NT2024

Schottky invariant diffusion on the transcendent p-adic upper half plane

Patrick Erik Bradley

The transcendent part of the Drinfeld p-adic upper half plane is shown to be a Polish space. Using Radon measures associated with regular differential 1-forms invariant under Schot…

cs.DM2024

Approximating Diffusion on Finite Multi-Topology Systems Using Ultrametrics

Patrick Erik Bradley, Angel Alfredo Moran Ledezma

Motivated by multi-topology building and city model data, first a lossless representation of multiple $T_{0}$ -topologies on a given finite set by a vertex-edge-weighted graph is give…

math.AP2024

A non-autonomous p-Adic diffusion equation on time changing graphs

Patrick Erik Bradley, Ángel Morán Ledezma

Motivated by the recently proven presence of ultrametricity in physical models (certain spin glasses) and the very recent study of Turing patterns on locally ultrametric state spac…

Searching Schemes With p-Adic Neumann Boundary Value Problems

Hearing Tamagawa Factors modulo q−1

p-Adic Diffusion and Random Walks on [0,1]

Neumann Boundary Value Problems on p-Adic Analytic Manifolds

Boundary Value Problems on p-Adic Analytic Manifolds

Hearing the Serre invariant of a compact p-adic analytic manifold

Boundary Value Problems for p-Adic Elliptic Parisi-Zúñiga Diffusion

Schottky invariant diffusion on the transcendent p-adic upper half plane

Approximating Diffusion on Finite Multi-Topology Systems Using Ultrametrics

A non-autonomous p-Adic diffusion equation on time changing graphs

Searching Schemes With $p$ -Adic Neumann Boundary Value Problems

Hearing Tamagawa Factors modulo $q - 1$

$p$ -Adic Diffusion and Random Walks on $[0, 1]$

Neumann Boundary Value Problems on $p$ -Adic Analytic Manifolds

Boundary Value Problems on $p$ -Adic Analytic Manifolds

Hearing the Serre invariant of a compact $p$ -adic analytic manifold