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 A. Vdovina
  Cayley graph expanders and groups of finite width
  Preprint (postscript)
  
  
• with M. Keller
  Cheeger constants, growth and spectrum of locally tessellating planar graphs
  Preprint (postscript)
  
  

Publications

• with E. Samiou
  Spherical spectral synthesis and two-radius theorems on Damek-Ricci spaces
  see at arXiv
  to appear in Arkiv för matematik
  
  
• with D. Lenz, O. Post and I. Veselic
  Continuity of the integrated density of states on random length metric graphs
  see at arXiv
  to appear in Mathematical Physics, Analysis and Geometry (online first)
  
  
• 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 (ongoing)
  
  
• 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 (see informations)

• Michaelmas term 2009/10: 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