University of Durham --- Department of Mathematical Sciences


Norbert Peyerimhoff

Department of Mathematical Sciences
Durham University
Science Laboratories
South Road
Durham, DH1 3LE

0191 334 3114
Department fax:
0191 334 3051

Research areas

In July 2019, I gave a lecture course ''Curvature Notions on Graphs'' in the LMS Undergraduate Summer School at the University of Leeds. Please click here for the lecture notes.

EPSRC Grant 2013-2016

Principal Investigator in the joint EPSRC grant EP/K016687/1 Topology, Geometry and Laplacians of Simplicial Complexes with Stefan Dantchev and Ioannis Ivrissimtzis (both School of Engineering and Computing Sciences, Durham University) and Alina Vdovina (School of Mathematics and Statistics, Newcastle University).

Our Research Associate was Shiping Liu. In October 2016, he moved as a "Thousand Youth Talents Program" Professor (特任教授,2016“青年千人计划”) to the School of Mathematical Sciences, University of Science and Technology of China (USTC), Hefei. Click here for his new homepage.

Research interests

My research interests are centered around geometry. Of particular interest are relations between geometry and Laplace- and Schrödinger operators and relations between geometry and dynamical systems. In most cases, the spaces under considerations are non-positively curved or have at least a noncompact covering space. I am also interested in analogues and differences between the continuous setting of Riemannian manifolds and the discrete setting of graphs, in explicit constructions of expander graphs, spectral graph theory, and synthetic curvature notions in discrete spaces. Recently, I also started a joint project with OlexSys, a crystallographic software company on campus, to investigate the exciting mathematical theory behind crystallography, and we are jointly supervising a PhD student (Laura Midgley).

Edited book


Dynamics and Analytic Number Theory, London Mathematical Society Lecture Note Series 437, eds. D. Badziahin, A. Gorodnik, N. Peyerimhoff, Cambridge University Press, 2016.

Written by leading experts, this book explores several directions of current research at the interface between dynamics and analytic number theory. Topics include Diophantine approximation, exponential sums, Ramsey theory, ergodic theory and homogeneous dynamics. The origins of this material lie in the 'Dynamics and Analytic Number Theory' Easter School held at Durham University in 2014. Key concepts, cutting-edge results, and modern techniques that play an essential role in contemporary research are presented in a manner accessible to young researchers, including PhD students. This book will also be useful for established mathematicians. The areas discussed include ubiquitous systems and Cantor-type sets in Diophantine approximation, flows on nilmanifolds and their connections with exponential sums, multiple recurrence and Ramsey theory, counting and equidistribution problems in homogeneous dynamics, and applications of thin groups in number theory. Both dynamical and 'classical' approaches towards number theoretical problems are also provided.

"Metric Diophantine approximation - aspects of recent work" by Victor Beresnevich, Felipe Ramírez and Sanju Velani
"Exponents of Diophantine approximation" by Yann Bugeaud
"Effective equidistribution of nilflows and bounds on Weyl sums" by Giovanni Forni
"Multiple recurrence and finding patterns in dense sets" by Tim Austin
"Diophantine problems and homogeneous dynamics" by Manfred Einsiedler and Tom Ward
"Applications of thin orbits" by Alex Kontorovich




Note: The papers listed here are not linked to retrievable files. If you want an offprint, let me know.

Authored book (German)

Mathematik in Anwendung mit C++, M. Hüttenhofer, M. Lesch, N. Peyerimhoff, Quelle & Meyer, UTB für Wissenschaft, 1994.

In diesem Buch werden ausgewählte Themen der Mathematik dargestellt, die sich besonders gut durch Algorithmen veranschaulichen lassen. Im zahlentheoretischen Teil des Buches geht es um die Teilbarkeit ganzer Zahlen und um Primzahlen -- eine Thematik, die in jüngster Zeit aufgrund moderner Verschlüsselungstechniken einen enormen Aufschwung erlebte. Polynome und die in den Naturwissenschaften bedeutsame Fouriertheorie sind Gegenstand des Analysis-Teils. Die Darstellung erstreckt sich von der Theorie bis zur kompletten Implementation in der Programmiersprache C++. Hierzu ist eine Begleitdiskette zum Buch beim Quelle & Meyer Verlag erhältlich. Eine ganze Reihe von Aufgaben und praktischen Beispielen dienen zur Vertiefung der vorgestellten Themen.

Supervision of Staatsexamens- and Diplomarbeiten in Bochum

PhD Supervision in Durham

English translation (by Femke Douma) of the article
E. Artin Ein mechanisches System mit quasiergodischen Bahnen
Hamburger Mathematische Abhandlungen 3 (1924), 170-175