Nikolai Dolbilin

Dolbilin

Graduated from Moscow State University, PhD at the Steklov Institute.
PhD thesis (advised by B.N. Delone (Delauney)): “On Dirichlet tessellation of the sphere”.
Doctorate thesis: “Regular and aperiodic structures in spaces with a constant curvature”.

Main affiliation:
1969 to present — works for the Steklov Mathematics Institute of the Russian Academy of Sciences, at present a leading research fellow.

Part-time work: :
  • Moscow State University, Kolmogorov Special Science Education Center № 18     —     1993-1998
  • Moscow State University, Department of Mechanics and Mathematics      —     1998 г.- present, Professor.
  • Yaroslavl State University, Discrete and Computational Geometry Laboratory      —     2011 – present, scientific fellow.

Academic activity (some):
  • Member at Large of the Executive Committee of the International Commission on Mathematical Education   —   2003-2007
  • Member of the PC of International Congress on Mathematical Education in Copenhagen      —     2001-2004
  • Member of the Russian Academy of Sci. commission on mathematics education      —     1985 — present.
  • Member on board of journal “Kvant”, vice-editor-in-chief      —     1980 — present.
  • Member of boards of journals “Contributions to Discrete Mathematics” (CDM), “Lobachevskii Mathematical Journal”, and “The Mathematical Intelligencer”.


Science interests and results (some):
1. Tilings, Delone sets and graphs: Local Theorems for regular and crystallographic tilings and sets, the extension theorem and criterion for stereohedra, theorem on the uncountability of aperiodic families, properties of parallelhedra.
2. Polyhedral manifolds and rigidity: established a theory of cubillages, a criterion of embedding of cubillages into the standard cube lattice, established rigidity of some classes of polyhedral spheres.
3. Combinatorial aspects of the Ising model: proved a presentation of the partition function of the Ising model for a lattice on a surface with genus g as the sum of 4g Pfaffians; for the Ising model on an arbitrary planar graph it was proved that the squared partition function equals the determinant of a generalized Kats—Ward matrix.