Alexey A. Tuzhilin
Full Professor of Mathematics
Department of Differential Geomatry and Applications
Faculty of Mechanics and Mathematics
Main Building, 1 Leninskiye Gory
Moscow, 119991, GSP-1,
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
- 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
- Ivanov A.O., Tuzhilin A.A. The Gromov-Hausdorff Distances between Simplexes and Ultrametric Spaces. 2019, ArXiv e-prints, arXiv:1907.03828.
Mikhaylov I.A. The Hausdorff Mapping Is Nonexpanding. 2017, ArXiv e-prints, arXiv:1710.08472.
- Problem. Solve generalized Borsuk problem for finite ultrametric spaces.
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 true that the Hausdorff mapping preserves GH-distance between a compact metric space and a simplex, both consisting of continuum number of points.
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. 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?
- 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.