Patrick Bradley

Since May 2022 I am a KIT Associate Fellow at the Institute of Photogrammetry and Remote Sensing at Karlsruhe Institute of Technology (KIT), Germany, where I am leading a research group "Mathematical Methods in Geodesy and Geoinformatics".

I received my PhD (Dr.rer.nat.) in 2002 at Universtät Karlsruhe (TH), the forerunner of KIT, under the supervision of Frank Herrlich in mathematics. Dissertation title: "p-adische Hurwitzräume" (p-adic Hurwitz spaces).

Email: <family name> (AT) kit.edu

My page at Institut für Photogrammetrie und Fernerkundung

My page at Geodätisches Institut Karlsruhe

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Research Areas

p-adic analysis, non-archimedean geometry and applications
mathematical methods in geodesy and geoinformatics
dynamics of the built environment

Other Areas of Interest

Romanian Byzantine Chant in various languages
Classical and Barocque Violoncello

Research Group "Mathematical Methods in Geodesy and Geoinformatics"

Current members

Angel Moran Ledezma, IPF, KIT (since Jan. 2023)
Riikka Kalmari, Tampere University, Finland (since May 2022)

Recent Research Projects

Entwicklung und beispielhafte Erprobung Mathematischer Methoden zur topologisch-algorithmischen Analyse der Vulnerabilität komplexer Gebäude mit Personenströmen im Brandfall. 2026-2029 [DFG].
Compact Ultrametric Analytic Manifolds and Applications in Number Theory. Habilitation Project. Since 2025.
p-Adic Analysis in Geometry and in the Mathematical Modelling of the Built Environment. Since 2019.
Verteilte Simulation von Prozessen in Bauwerken und Stadtmodellen (Distributed Simulation of Processes in Buildings and City Models). 2021-2026 [DFG].
Topological consistent modeling in spatio-temporal context with moving objects in the city model. 2017-2021 [DFG].

Teaching (Courses for "Geodäsie und Geoinformatik" and "Remote Sensing and Geo-Informatics")

Grundlagen der Statistik, Vorlesung und Übung (2+1 SWS), GuG BSc. WiSe

Geometrische Modelle der Geodäsie, Vorlesung und Übung (2+1 SWS), GuG BSc. WiSe

Physikalische Modelle der Geodäsie, Vorlesung und Übung (2+1 SWS), GuG BSc. SoSe

Numerical Mathematics, Lecture and Exercises (3+1 SWS), GuG MSC. + RSGI MSc. WiSe

Current PhD students

Riikka Kalmari. Dynamic flows of the Finnish building stock. PhD student at Tampere University (Finland) since May 2022.

Past PhD students

Angel Moran Ledezma. Ultrametric Spaces: Spectral and Stochastic Methods with Applications in Science. Karlsruhe Institute of Technology (2026)

Markus Jahn. Distributed and Parallel Data Management to Support Geo-Scientific Simulation Implementations. Karlsruhe Institute of Technology (2022)

Anna Giovanella. Automatische redundanzfreie Generierung von Topologie aus multidimensionalen geographischen Datenbeständen. Karlsruhe Institute of Technology (2022)

Norbert Paul. Topologische Datenbanken für Architektonische Räume. Dissertation. Universität Karlsruhe (2008)

Reviewed PhD theses

Juan Pablo Velasquez. Harmonic Analysis in profinite groups (Analisis armonico en grupos pro-finitos). Universidad del Valle (Columbia), 2025.

Supervised Final and Student Theses

Paulina Halwas. The Trees Associated with the Transcendental p-adic Numbers. Bachelor's Thesis. Karlsruhe Institute of Technology (2025)

Matthieu Rebmeister. Parameter Estimation for Persistent Scatterer Interferometry using Compressive Sensing. Master's Thesis. Karlsruhe Institute of Technologie (2020)

Anna Krimmelbein. Topologie in CityGML. Diplom Thesis. Karlsruhe Institute of Technologie (2011)

Anna Krimmelbein. Topologie von Graphen im Kontext der Geoinformatik. Student Thesis. Karlsruhe Institute of Technologie (2010)

Martin Behnisch. Klassifizierung von Gemeinden nach bestandsorientierten Merkmalen. Diplom Thesis. Universität Karlsruhe (2004)

Pablo Viejo García. Ettlingen. Vergangenheit, Gegenwart, Zukunft. Diplom Thesis. Universität Karlsruhe (2003)

Preprints

P.E. Bradley. Searching Schemes With p-Adic Neumann Boundary Value Problems. arXiv:2609.27751 [math.AG], 2026
P.E. Bradley. Neumann Boundary Value Problems on p-Adic Analytic Manifolds. arXiv:2609.26180 [math.AP], 2026
P.E. Bradley. Hearing Tamagawa Factors modulo q-1. arXiv:2608.05868 [math.NT], 2026
P.E. Bradley, P. Halwas, E.A. Nitsche, A.M. Ledezma. p-Adic Diffusion and Random Walks on [0,1]. arXiv:2608.02103 [math.PR], 2026
P.E. Bradley. Boundary Value Problems on p-Adic Analytic Manifolds. arXiv:2605.16590 [math.NT], 2026
P.E. Bradley and A. Moran Ledezma. Approximating Diffusion on Finite Multi-Topology Systems Using Ultrametrics. arXiv:2411.00806 [cs.DM], 2024

Selected Publications

P.E. Bradley and A. Moran Ledezma. Hearing the Serre invariant of a compact p-adic analytic manifold. Mathematische Nachrichten, 299 (10), 3126–3138, 2026
P.E. Bradley. Diffusion operators on p-adic analytic manifolds. Results in Mathematics, 81 (5), 129, 2026
P.E. Bradley. Local ultrametric approximation of graph distance based Laplacian diffusion. Reports on Mathematical Physics, 97(1):115-142, 2026
P.E. Bradley. Boundary Value Problems for p-Adic Elliptic Parisi-Zúñiga Diffusion. Journal of Pseudodifferential Operators and Applications, 17:9, 2026
P.E. Bradley. Schottky invariant diffusion on the transcendent p-adic upper half plane. Nonlinear Analysis, 263:113947, 2026
P.E. Bradley. Vladimirov-Pearson Operators on ζ-regular Ultrametric Cantor Sets. Mathematische Nachrichten, 298(12):3613-4016, 2025
P.E. Bradley. Heat Equations and Hearing the Genus on p-adic Mumford Curves via Automorphic Forms. Moscow Mathematical Journal, 25(4):1-32, 2025
P.E. Bradley. On the local ultrametricity of finite metric data. Journal of Classification, 42(3):624-638, 2025
P.E. Bradley and A. Moran Ledezma. A non-autonomous p-adic diffusion equation on time changing graphs. Reports on Mathematical Physics, 95(2):155-180, 2025
P.E. Bradley. Topological Applications of p-Adic Divergence and Gradient Operators. Journal of Mathematical Physics, 66:021504, 2025
P.E. Bradley. Schottky-Invariant p-Adic Diffusion Operators. Journal of Fourier Analysis and Applications, 31(1):8, 2025
P.E. Bradley. Theta-induced diffusion on Tate elliptic curves over non-archimedean local fields. Pacific Journal of Mathematics, 334(1):13-42, 2025
P.E. Bradley and A. Moran Ledezma. Hearing Shapes via p-Adic Laplacians. Journal of Mathematical Physics, 64:113502, 2023
P.E. Bradley. Heat Equations and Wavelets on Mumford Curves and Their Finite Quotients. Journal of Fourier Analysis and Applications, 29:62, 2023
P.E. Bradley. p-Adic wave equations on finite graphs and T0-spaces. In W.A. Zuniga-Galindo and B. Toni, editors, Advances in Non-Archimedean Analysis and Applications, pages 275–295. Springer International Publishing, 2021
P.E. Bradley. Generalised diffusion on moduli spaces of p-adic Mumford curves. p-Adic Numbers, Ultrametric Analysis, and Applications, 12(2):73– 89, 2020.
P.E. Bradley. On the logistic behaviour of the topological ultrametricity of data. Journal of Classification, 36:266–272, 2019
P.E. Bradley. Finding ultrametricity in data using topology. Journal of Classification, 34(1):76–84, 2017
P.E. Bradley. Ultrametricity indices for the euclidean and boolean hypercubes. p-Adic Numbers, Ultrametric Analysis, and Applications, 8(4):298– 311, 2016
P.E. Bradley. A p-adic RANSAC algorithm for stereo vision using Hensel lifting. p-Adic Numbers Ultrametric Analysis, and Applications, 2(1):55–67, 2010
P.E. Bradley. From image processing to topological modelling with p-adic numbers. p-Adic Numbers, Ultrametric Analysis, and Applications, 2(4): 293-304, 2010
P.E. Bradley. Mumford dendrograms and discrete p-adic symmetries. p-Adic Numbers, Ultrametric Analysis, and Applications, 1(2):118–127, 2009
P.E. Bradley. Cyclic coverings of the p-adic projective line by Mumford curves. manuscripta mathematica, 124:77–95, 2007
P.E. Bradley. Riemann existence theorems of Mumford type. Mathematische Zeitschrift, 251(2):393–414, 2005
P.E. Bradley. p-adische Hurwitzräume. Dissertation. Universität Karlsruhe, 2002

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Patrick Bradley

Entwicklung und beispielhafte Erprobung Mathematischer Methoden zur topologisch-algorithmischen Analyse der Vulnerabilität komplexer Gebäude mit Personenströmen im Brandfall. 2026-2029 [DFG].

Compact Ultrametric Analytic Manifolds and Applications in Number Theory. Habilitation Project. Since 2025.

p-Adic Analysis in Geometry and in the Mathematical Modelling of the Built Environment. Since 2019.

Verteilte Simulation von Prozessen in Bauwerken und Stadtmodellen (Distributed Simulation of Processes in Buildings and City Models). 2021-2026 [DFG].

Topological consistent modeling in spatio-temporal context with moving objects in the city model. 2017-2021 [DFG].