Norbert Peyerimhoff
Department of Mathematical Sciences
Durham University
Science Laboratories
South Road
Durham, DH1 3LE
 Phone:
 0191 334 3114
 Department fax:
 0191 334 3051
 email:

norbert.peyerimhoff@durham.ac.uk
Research areas
 Spectral Geometry
 Schrödinger operators
 Symmetric Spaces
 Dynamical Systems
 Graph Theory
EPSRC grant
Principal Investigator in the joint EPSRC
grant 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
is Shiping Liu.
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
nonpositively 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 and spectral graph theory.

Preprints

Publications
 with E. Samiou
The Xray transform on
2step nilpotent Lie groups of higher rank , 2016
 with Sh. Liu and F. Münch
Curvature and higher
order Buser inequalities for the graph connection Laplacian,
2015, MPIM preprint 2016(3)
 with M. Keller and F. Pogorzelski
Sectional curvature of polygonal
complexes with planar substructures, 2014
 with Sh. Liu and A. Vdovina
Signatures, lifts, and
eigenvalues of graphs, 2014
 with Sh. Liu
Eigenvalue ratios of nonnegatively curved graphs, 2014
 with G. Knieper
Noncompact harmonic manifolds, 2013
Oberwolfach Preprints 201308
 with I. Ivrissimtzis and A. Vdovina
Trivalent expanders and hyperbolic surfaces, 2012
Note: The papers listed here are not linked to retrievable
files. If you want an offprint, let me know.
 with C. Lange, Sh. Liu and O. Post
Frustration index and Cheeger inequalities for discrete and continuous magnetic Laplacians
Calculus of Variations and Partial Differential Equations 54 (2015), 41654196.
 with N. Barker, N. Boston and A. Vdovina
Regular algebraic surfaces, ramification structures and projective
planes
Beauville surfaces and groups, Springer
Proc. Math. Stat., 123, 2015, pp. 1533
 with K. Leonhardt, M. Tautenhahn and I. Veselic
Wegner estimate and localization for alloytype models with signchanging exponentially decaying singlesite potentials
Reviews in Mathematical Physics 27 (2015), 45pp
 with G. Knieper
Geometric properties of rank one asymptotically harmonic manifolds
Journal of Differential Geometry 100 (2015), 507532, see also arXiv:1307.0629
 with G. Knieper
Harmonic functions on rank one asymptotically harmonic manifolds
arXiv:1404.4290, see also Journal of Geometric Analysis, published online, 03 February 2015
 with N. Barker, N. Boston and A. Vdovina
An infinite family of 2groups with mixed Beauville structure
International Mathematics Research Notices 11 (2015), 35983618
 with E. Samiou
Integral Geometric Properties of Noncompact Harmonic Spaces
Journal of Geometric Analysis 25 (2015), 122148
 Y. Yang, N. Peyerimhoff and I. Ivrissimtzis
Linear correlations between spatial and normal noise in triangle meshes
IEEE Transactions on Visualization and Computer Graphics 19 (2013), no. 1, 4555
 with I. Ivrissimtzis
Spectral representations of vertex transitive graphs, Archimedean solids and finite Coxeter groups
arXiv:1106.2509
Groups, Geometry and Dynamics 7
(2013), no. 3, 591615
 with K. Gittins, M. Stoiciu and D. Wirosoetisno
Some spectral applications of McMullen's Hausdorff dimension algorithm
arXiv:1112.1020
Conformal Geometry and Dynamics 16 (2012), 184203
 with N. Barker, N. Boston and A. Vdovina
New examples of Beauville surfaces
Monatshefte für Mathematik 166 (2012), no. 34, 319327
 with A. Vdovina
Cayley graph expanders and groups of finite width
Journal of Pure and Applied Algebra 215 (2011), no. 11, 27802788
 with S. Castle and K. F. Siburg
Billiards in ideal hyperbolic polygons
Discrete and
Continuous Dynamical Systems A 29 (2011), no. 3, 893908
 with M. Keller
Cheeger constants, growth and spectrum of locally tessellating planar graphs
Mathematische Zeitschrift 268 (2011), no. 34,
871886
 with E. Samiou
Spherical spectral synthesis and tworadius theorems on DamekRicci spaces
Arkiv för matematik 48 (2010), no. 1, 131147
 with D. Lenz, O. Post and I. Veselic
Continuity of the integrated density of states on random length metric graphs
Mathematical Physics, Analysis and Geometry 12 (2009), no. 3, 219254
 with D. Lenz, O. Post and I. Veselic
Continuity properties of the integrated density of states on manifolds
Japanese Journal of Mathematics 3 (2008), Issue 1, 121161
 with G. Knieper
Ergodic properties of isoperimetric domains in spheres
Journal of Modern Dynamics 2 (2008), no. 2, 339358
 with D. Lenz, I. Veselic
Groupoids, von Neumann algebras and the integrated density of states
Mathematical Physics, Analysis and Geometry 10 (2007), no. 1, 141
 with L. Karp
Geometric heat comparison criteria for Riemannian manifolds
Annals of Global Analysis and Geometry 31 (2007), 115145
 with O. Baues
Geodesics in nonpositively curved plane tesselations
Advances of Geometry 6 (2006), no. 2, 243263
 with S. Klassert, D. Lenz, P. Stollmann
Elliptic operators on planar graphs: unique continuation for
eigenfunctions and nonpositive curvature
Proc. Amer. Math. Soc. 134 (2006), no. 5, 15491559
 Spherical means on compact locally symmetric spaces of nonpositive
curvature
Forum Mathematicum 18 (2006), no. 3, 391417
 with D. Lenz, I. Veselic
Integrated density of states for random metrics on manifolds
Proc. Lond. Math. Soc. (3) 88 (2004), no. 3, 733752
 with E. Samiou
The Cheeger constant of simply connected, solvable Lie groups
Proc. Amer. Math. Soc. 132 (2004), no. 5, 15251529
 with D. Lenz, I. Veselic
Random Schrödinger operators on manifolds
Markov Processes and Related Fields 9 (2003), no.
4, 717728
(Special issue containing contributions by participants of the conference
Mathematical aspects of random systemes and statistical mechanics,
Mai 2002, CIRMLuminy
in the honour of Leonid Pastur)
 with K.F. Siburg
The dynamics of magnetic flows for energies above Mane's critical
value
Israel Journal Math. 135 (2003), 269298
 Simplices of maximal volume or minimal total edge length
in hyperbolic space
Journal Lond. Math. Soc. (2) 66 (2002), no. 3, 753768
 with I. Veselic
Integrated density of states for ergodic random Schrödinger
operators on manifolds
Geom. Dedicata 91 (2002), 117135
 with L. Karp
Extremal properties of the principal Dirichlet eigenvalue for
regular polygons in the hyperbolic plane
Arch. Math. 79 (2002), no.3, 223231
 Isoperimetric and ergodic properties of horospheres in
symmetric spaces
Proc. Symp. Pure Math. 69
in: Smooth Ergodic Theory and its Applications
Amer. Math. Soc. (2001)
 with O. Baues
Curvature and geometry of tesselating plane graphs
Discrete Comput. Geom. 25 (2001), no. 1, 141159
 with L. Karp
Spectral gaps of Schrödinger operators on hyperbolic space
Math. Nachrichten 217 (2000), 105124
 with L. Karp
Horospherical means and uniform distribution of curves of constant
geodesic curvature
Math. Zeitschrift 231 (1999), no. 4, 655677
 with L. Karp
On the distribution of hypersurfaces equidistant from totally
geodesic submanifolds in hyperbolic space
Analysis 18 (1998), no. 3, 217225
 with M. Lesch
On index formulas for manifolds with metric horns
Commun. Partial Differ. Equations 23 (1998), no. 34, 649684
 Areas and intersections in convex domains
Amer. Math. Monthly 104 (1997), no. 8, 697704
 with M. Hüttenhofer, M. Lesch
Mathematik in Anwendung mit C++
Algorithmen aus Analysis und Zahlentheorie
UTB für Wissenschaft, Uni Taschenbücher 1816 (1994)
 with J. Brüning, H. Schröder
The $\overline{\partial}$operator on algebraic curves
Commun. Math. Phys. 129 (1990), no. 3, 525534
 Kerstin Danneberg (Staatsexamensarbeit, October 2002)
 Annika Hass (Staatsexamensarbeit, October 2002)
 Barbara Hermey (Staatsexamensarbeit, October 2002)
 Thorsten Henkel (Diplomarbeit, March 2004)
 Sandra Zeidler (Staatsexamensarbeit, October 2004)
 Nina Maus (Diplomarbeit, October 2005)
 Femke Douma (completed on April 2010)
 Michela Egidi (joint supervision with O. Post, completed on November 2015)
English translation (by Femke Douma) of the article
E. Artin Ein mechanisches System mit
quasiergodischen Bahnen
Hamburger Mathematische
Abhandlungen 3 (1924), 170175

Epiphany term 2004/05: 3H/4H Geometry

Michaelmas term 2005/06: Msc Course Measure Theory and Dynamics (see information)

Epiphany term 2005/06: 3H/4H Algebraic Geometry

Epiphany term 2005/06: 2H Contours and Hyperbolic Geometry (see information)

Michaelmas/Epiphany term 2006/07: 4H Riemannian Geometry

Epiphany term 2007/08: 3H/4H Analysis

Michaelmas term 2008/09: 3H/4H Geometry (see information)

Michaelmas term 2008/09: 4H Riemannian Geometry

Michaelmas and Epiphany terms 2009/10: 3H/4H Analysis

Michaelmas and Epiphany terms 2010/11: 4H Riemannian Geometry
(see
information)

Michaelmas and Epiphany terms 2011/12: 3H/4H Analysis
(see information)

Michaelmas term 2012/13: 1H Core B2: Problem Solving

Michaelmas term 2012/13: 3H Differential Geometry

Michaelmas term 2013/14: 1H Core B2: Problem Solving
(see
information)

Epiphany term 2013/14: 3H/4H Algebraic Geometry
(see
information)

Michaelmas term 2014/15: 1H Core B1: Analysis

Epiphany term 2014/15: 1H Core B1: Analysis

Michaelmas term 2015/16: 1H Core B1: Analysis

Epiphany term 2015/16: 1H Core B1: Analysis
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