Dr. Norbert Peyerimhoff

Phone:

0191 334 3114

Department fax:

0191 334 3051

e-mail:

norbert.peyerimhoff@durham.ac.uk

Research areas

• Spectral Geometry
  
• Schrödinger operators
  
• Symmetric Spaces
  
• Dynamical Systems
  
• Graph Theory
  

Research interests

Preprints

Publications

Publications with abstract

Preprints

• with K. Gittins, M. Stoiciu and D. Wirosoetisno
  Some spectral applications of McMullen's Hausdorff dimension algorithm
  arXiv:1112.1020
  
  
• with N. Barker, N. Boston and A. Vdovina
  Regular algebraic surfaces isogenous to a higher product constructed from group representations using projective planes
  arXiv:1109.6053
  
  
• with I. Ivrissimtzis
  Spectral representations of vertex transitive graphs, Archimedean solids and finite Coxeter groups
  arXiv:1106.2509
  
  

Publications

• with N. Barker, N. Boston and A. Vdovina
  New examples of Beauville surfaces
  Monatshefte für Mathematik, Online First, 5 February 2011
  
  
• with A. Vdovina
  Cayley graph expanders and groups of finite width
  Journal of Pure and Applied Algebra 215 (2011), no. 11, 2780-2788
  
  
• with S. Castle and K. F. Siburg
  Billiards in ideal hyperbolic polygons
  Discrete and Continuous Dynamical Systems A 29 (2011), no. 3, 893-908
  
  
• with M. Keller
  Cheeger constants, growth and spectrum of locally tessellating planar graphs
  Mathematische Zeitschrift 268 (2011), no. 3-4, 871-886
  
  
• with E. Samiou
  Spherical spectral synthesis and two-radius theorems on Damek-Ricci spaces
  Arkiv för matematik 48 (2010), no. 1, 131-147
  
  
• 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, 219-254
  
  
• 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, 121-161
  
  
• with G. Knieper
  Ergodic properties of isoperimetric domains in spheres
  Journal of Modern Dynamics 2 (2008), no. 2, 339-358
  
  
• with D. Lenz, I. Veselic
  Groupoids, von Neumann algebras and the integrated density of states
  Mathematical Physics, Analysis and Geometry 10 (2007), no. 1, 1-41
  
  
• with L. Karp
  Geometric heat comparison criteria for Riemannian manifolds
  Annals of Global Analysis and Geometry 31 (2007), 115-145
  
  
• with O. Baues
  Geodesics in non-positively curved plane tesselations
  Advances of Geometry 6 (2006), no. 2, 243-263
  
  
• 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, 1549-1559
  
  
• Spherical means on compact locally symmetric spaces of non-positive curvature
  Forum Mathematicum 18 (2006), no. 3, 391-417
  
  
• with D. Lenz, I. Veselic
  Integrated density of states for random metrics on manifolds
  Proc. Lond. Math. Soc. (3) 88 (2004), no. 3, 733-752
  
  
• with E. Samiou
  The Cheeger constant of simply connected, solvable Lie groups
  Proc. Amer. Math. Soc. 132 (2004), no. 5, 1525-1529
  
  
• with D. Lenz, I. Veselic
  Random Schrödinger operators on manifolds
  Markov Processes and Related Fields 9 (2003), no. 4, 717-728
  (Special issue containing contributions by participants of the conference
  Mathematical aspects of random systemes and statistical mechanics, Mai 2002, CIRM-Luminy
  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), 269-298
  
  
• Simplices of maximal volume or minimal total edge length in hyperbolic space
  Journal Lond. Math. Soc. (2) 66 (2002), no. 3, 753-768
  
  
• with I. Veselic
  Integrated density of states for ergodic random Schrödinger operators on manifolds
  Geom. Dedicata 91 (2002), 117-135
  
  
• with L. Karp
  Extremal properties of the principal Dirichlet eigenvalue for regular polygons in the hyperbolic plane
  Arch. Math. 79 (2002), no.3, 223-231
  
  
• 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, 141-159
  
  
• with L. Karp
  Spectral gaps of Schrödinger operators on hyperbolic space
  Math. Nachrichten 217 (2000), 105-124
  
  
• with L. Karp
  Horospherical means and uniform distribution of curves of constant geodesic curvature
  Math. Zeitschrift 231 (1999), no. 4, 655-677
  
  
• with L. Karp
  On the distribution of hypersurfaces equidistant from totally geodesic submanifolds in hyperbolic space
  Analysis 18 (1998), no. 3, 217-225
  
  
• with M. Lesch
  On index formulas for manifolds with metric horns
  Commun. Partial Differ. Equations 23 (1998), no. 3-4, 649-684
  
  
• Areas and intersections in convex domains
  Amer. Math. Monthly 104 (1997), no. 8, 697-704
  
  
• 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, 525-534
  
  

Supervision of Staatsexamens- and Diplomarbeiten in Bochum

• Kerstin Danneberg (Staatsexamensarbeit, October 2002)
  
  
• Annika Hass (Staatsexamensarbeit, October 2002)
  
  
• Barbara Hermey (Staatsexamensarbeit, October 2002)
  
  
• Christiane Siburg (Staatsexamensarbeit, May 2003)
  
  
• Thorsten Henkel (Diplomarbeit, March 2004)
  
  
• Sandra Zeidler (Staatsexamensarbeit, October 2004)
  
  
• Nina Maus (Diplomarbeit, October 2005)
  
  

PhD Supervision in Durham

• Femke Douma (completed on April 2010)
  
  
• Andy Hayden (joint supervision with J.R. Parker)
  
  

Teaching

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

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

• Epiphany term 2005/06: 3H/4H Algebraic Geometry (see informations)

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

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

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

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

• 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 informations)

• Michaelmas and Epiphany terms 2010/11: 3H/4H Analysis (see informations)

Links:

• Durham Pure Mathematics Home page
  (formal page).
• Durham Pure Mathematicians' page
  (intended for members of the department but open to all).
• Department of Mathematical Sciences home page.
• The University of Durham home page