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

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.