Alexey Tuzhilin



1997  Doctor Phys.-Math. Science (habilitation), Dissertation Classification of Local Minimal Planar Networks  with Convex Boundaries.

1990 Candidate  Phys.-Math. Science (PhD), Dissertation Morse's Indices of Minimal Surfaces. Sci. Advisor  Prof. A. Fomenko.


From 2009 Member of Academic Council of Faculty of Mechanics and Mathematics, Moscow State University

From 2007 Member of Experts Council of Superior Certification Commission

From 2006 Head of Laboratory of Computer Methods in Humanities and Natural Sciences, Faculty of Mechanics and Mathematics, Moscow State University

From 2000  Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, department of Differential geometry and applications, professor; Moscow Institute of Physics and Technology, professor.  


Research interests: topological and geometrical variational problems, extreme networks theory, in particular, branching geodesics and Steiner problem on Riemannian manifolds and Alexandrov surfaces, Steiner ratio and Gilbert-Pollak conjecture, graph theory, computer geometry, metric  geometry, mathematical biology.   


Current research:

Minimal fillings (in the sense of M.Gromov) for finite metric spaces by weighted graphs. Some general properties described, minimal fillings constructed for some special cases (generalized additive spaces), a general formula for the weight of minimal filling is conjectured, relations between minimal fillings and shortest networks are obtained.

Interior spanning trees for plane polygons and plane immersed polygons. There investigated a generalization of Voronoi diagram and Delaunay triangulation concepts for these cases. Description of possible Delaunay cells is obtained.


Pedagogical activities:

Lecture Courses on High Geometry and Topology (Moscow Institute of Physics and Technology), Visual Geometry (MSU); Special Lecture Courses on Geometrical Graph Theory, Metric Geometry, Extreme Networks Theory; Practical training:  Computer geometry. 


Current scientific advising: 

1 third year student, 1 fourth year students, 3 fifth year (graduate) students,  1 post-graduate  students. Three of my post graduate students obtained their PhD degrees. 



I have more than 100 scientific publications including 5 monographs and 2 textbooks. 

Ten recent publications:

  1. Ivanov, A.O.; Tuzhilin, A.A. Immersed polygons and their diagonal triangulations. Izvestiya: Mathematics, 2008, 72:1, 63–90.
  2. Ivanov A.O., Ilyutko D.P., Nosovski G.V., Tuzhilin A.A., Fomenko A.T. Computer modeling of curves and surfaces. Fundament. i Prikl. Matem., 2009, 15:5,  63–94 (Journal of Mathematical Sciences (New York), 2011, 172:5, 663–689).
  3. Ivanov A.O., Tuzhilin A.A.  The Length of a Minimal Tree With a Given Topology: generalization of Maxwell Formula. arXiv:1101.2117v1 [math.MG] (; Vestnik MGU, Ser. Math., no.3, pp.7-14 (2010).
  4. Ivanov A.O., Tuzhilin A.A. Minimal fillings in the sense of M.Gromov for finite metric spaces, International Conference “Metric Geometry of surfaces and polyhedra” dedicated to 100th anniversary of N.V.Efimov, 2010, p. 74.
  5. Ivanov A.O.,Ilyutko D.P., Nosovski G.V., Tuzhilin A.A., Fomenko A.T. Computer Geometry: Practical Training. Moscow, BINOM, 2010, 392 pp. [in Russian]. 
  6. Ivanov A.O., Tuzhilin A.A.  One-dimensional Gromov minimal filling. arXiv:1101.0106v2 [math.MG] (; Matemat. sbornik 2012 (to appear).
  7. Ivanov A.O., Tuzhilin A.A.  Geometry of inner spanning trees for plane polygons. Izvestija RAN, 2011,  to appear. 
  8. Ivanov A.O., Ovsyannikov Z.N., Strelkova N.P., Tuzhilin A.A.  One-dimensional minimal fillings with negative edge weights. arXiv:1101.3014v1 [math.MG] (; Vestnik MGU, Ser Matem., Mekh., 2012, to appear.
  9. Bozhenko V.K., Ivanov A.O., Mishchenko A.S., Tuzhilin A.A., Shishkin A.M. Determination of Different Biological Factors on the Base of Dried Blood Spot Technology, arXiv:1101.2576v1 [math.ST]  (
  10. Ivanov A.O., Tuzhilin A.A. The Steiner Ratio Gilbert–Pollak Conjecture Is Still Open. Clarification Statement. Algorithmica, 2011, DOI: 10.1007/s00453-011-9508-3.




Department of Differential Geometry and Applications

Faculty of Mechanics and Mathematics, 

Moscow State University named for M.V.Lomonosov,

Leninskie Gory 1, 

Moscow, 199991, Russia 

+7(495)9393940 office

+7(495)3342870 home

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