Alexey A. Tuzhilin

Full Professor of Mathematics

                    Department of Differential Geomatry and Applications
                    Faculty of Mechanics and Mathematics
                           Lomonosov Moscow State University
                           Main Building, 1 Leninskiye Gory
                           Moscow, 119991, GSP-1, 
                           Russia
                           Phone: +7-495-939-3940
                           E-mail: tuz@mech.math.msu.su


Curriculum Vitae

• Biographical Information
• Publications
• Student research supervision
• Recent Talks

Areas of Interest

Alexey Tuzhilin investigates low-dimensional geometrical variational problems, including various generalizations of Steiner Problem on finding shortest networks (Steiner minimal trees). He pays special attention to one-dimensional minimal fillings in Gromov’s sense. In addition, he researches on the geometry of Gromov-Hausdorff space, i.e., the space of isometry classes of compact metric spaces. Alexey Tuzhilin obtained his main results in collaboration with Alexander O. Ivanov.

Books In English

Certificates of Reviewing

Degrees

• MA, Moscow State University,  1985
• PhD, Moscow State University, 1990
• ScD, Moscow State University, 1997

Awards

• State gratuity for young scientists, 1996, Moscow, Russia
• Shuvalov premium, 2000, Moscow, Russia
• Russian Federation President Grant "Young doctors of science", 2001, Moscow, Russia
• Euler gratuity, 2002, Bochum, Germany

Lectures on Hausdorff and Gromov-Hausdorff Distances Geometry

• Chapter 1. Elements of general topology.
•  Exercises to Chapter 1.
• Chapter 2. Introduction to metric spaces.
•  Exercises to Chapter 2.
• Chapter 3. Curves in metric spaces.
•  Exercises to Chapter 3.
• Chapter 4. Extreme graphs and networks.
• Chapter 5. Hausdorff distance.
• Chapter 6. Gromov-Hausdorff distance.
• Chapter 7. Gromov-Hausdorff space.
• Chapter 8. Calculating GH-distances to simplexes and some applications.

Examination

1. Ivanov A.O., Tuzhilin A.A. The Gromov-Hausdorff Distances between Simplexes and Ultrametric Spaces. 2019, ArXiv e-prints, arXiv:1907.03828.
•  Problem. Solve generalized Borsuk problem for finite ultrametric spaces.
2. Mikhaylov I.A. The Hausdorff Mapping Is Nonexpanding. 2017, ArXiv e-prints, arXiv:1710.08472.
•  Problem. Is it true that the Hausdorff mapping preserves GH-distance between a compact metric space and a simplex, both consisting of continuum number of points.
3. Ivanov A.O., Iliadis S., Tuzhilin A.A. Local Structure of Gromov-Hausdorff Space, and Isometric Embeddings of Finite Metric Spaces into this Space. 2016, ArXiv e-prints, arXiv:1604.07615.
•  Problem. Is it possible isometrically embed any 3-point (4-point) metric space in GH-space in such a way that the images of its points are simplexes?
4. Ivanov A.O., Tuzhilin A.A. Local Structure of Gromov-Hausdorff Space near Finite Metric Spaces in General Position. 2016, ArXiv e-prints, arXiv:1611.04484.
•  Problem. Let Dn be a simplex with n points. Prove that 1/2-open balls in GH-space with the centers at D1 and D2 are not isometric.