Alexander O. Ivanov

1. Life and career

Alexander O. Ivanov was born on 14 August 1963 in the town of Opochka, Pskov Region, into a family of Moscow employees. In 1980 he finished secondary school No. 40 in Moscow and entered the Faculty of Mechanics and Mathematics of MSU, graduating in 1985. His diploma work was written under the supervision of A. T. Fomenko.

During his student years he took an active part in the student construction brigade movement: from 1983 he regularly went with the brigade “Slavyane” to Smolensk Region, working as a team leader, commissar and commander of the brigade.

After completing the postgraduate programme in 1988 he was assigned to the Bauman Moscow State Technical University (MSTU) at the Department of Applied Mathematics as assistant professor (head of the Department: Professor V. S. Zarubin), while continuing to take part in the seminars of the Faculty of Mechanics and Mathematics of MSU. In 1990 he defended his candidate dissertation and received the position of docent; he lectured on discrete mathematics at the faculties of MSTU.

Since 1992 he has worked at the Faculty of Mechanics and Mathematics of MSU, at the Department of Differential Geometry and Applications, first as assistant and then as docent. In 1998 he defended his doctoral dissertation. Since 2000 he has been Professor at the Department (participant of the MSU Rector's programme “100+100”). In 2019 he received the title of Professor in the specialty “Geometry and Topology”.

Over the years he has taught the courses “Classical Differential Geometry”, “Differential Geometry and Topology” and “Visual Geometry and Topology”, as well as special courses on metric geometry and geometric optimisation. He supervises the research work of students and postgraduate students and has trained 7 candidates of sciences.

He continues to cooperate with Bauman MSTU, where he is Professor (part-time) at the Department of Mathematical Modelling, and is Deputy Head of the Department of Differential Geometry and Applications. For a number of years he was academic secretary of the Dissertation Council D 501.001.84 at MSU and deputy dean for work with foreign students; since 2020 he has been deputy dean for research.

He coordinates the cooperation of the Faculty of Mechanics and Mathematics with the Sino-Russian Mathematical Center and the Sino-Russian Association of Fundamental Sciences (SRAFS), and the Summer Undergraduate International Mathematical Summer Schools of the four leading universities of Asia, regularly held in Moscow, Beijing, Seoul and Tokyo.

2. Degrees and positions

3. Research

A. O. Ivanov is a specialist known in Russia and abroad in topological calculus of variations and the theory of extremal networks, in particular branching geodesics and the Steiner problem, minimal fillings of finite metric spaces, graph theory, computer geometry and metric geometry, including the geometry of hyperspaces with the Gromov–Hausdorff distance.

His candidate dissertation “Minimal surfaces and calibration forms” (advisor A. T. Fomenko) was devoted to singularities of multidimensional minimal surfaces with symmetries. A. O. Ivanov applied the methods of calibration forms created by R. Harvey and H. B. Lawson to the case of manifolds with symmetries; the new examples of globally minimal cones of large codimension that he constructed attracted considerable interest among specialists in the multidimensional Plateau problem.

Later his interests concentrated on the classical Steiner problem (the one-dimensional analogue of the Plateau problem) and its generalizations. A. O. Ivanov is one of the authors of the theory of branching extremals of one-dimensional variational problems, which arose at the junction of differential geometry, the calculus of variations and graph theory in an attempt to find a geometric approach to the Steiner problem. It made it possible to discover a number of new geometric effects and to establish relations between the geometry of boundary sets and the topology of extremal networks, and between the structure of extremal networks and metric and topological characteristics of the ambient manifold. Possible applications include transportation problems, molecular biology, the theory of evolution, mathematical economics and the theory of nanosystems.

A. O. Ivanov and A. A. Tuzhilin introduced fillings of finite metric spaces, generalizing Gromov's notion of a filling of a Riemannian manifold. A connected weighted graph containing a finite metric space as a subset of its vertex set is its filling if the distance along the graph is not less than in the original space; minimal fillings turned out to be closely related to shortest trees, and the weight of a minimal filling gives a lower bound for the length of the shortest tree with the same boundary. The weight of a minimal filling can be found by a minimax formula in which the maximum is taken over the vertices of a multidimensional convex polyhedron constructed from the type of the filling.

Recently A. O. Ivanov and A. A. Tuzhilin have also been interested in the geometry of hyperspaces: metric spaces whose points are subsets of a given metric space and, more generally, metric spaces themselves (with the Hausdorff and Gromov–Hausdorff distances respectively). The interest is caused both by the beauty and complexity of the mathematical constructions and by a wide range of applications such as comparison and recognition of images and modelling of enzyme docking. A. O. Ivanov with colleagues also works on applied problems connected with image comparison, signal enhancement and video processing; under his supervision three successful commercial projects with Huawei Technologies have been carried out.

4. Publications (selected)

Full list of publications — 229 records (department page and ISTINA profile)

Monographs and textbooks

1. A. O. Ivanov, A. A. Tuzhilin. Minimal Networks. The Steiner Problem and Its Generalizations. CRC Press, 1994.
2. A. O. Ivanov, A. A. Tuzhilin. Branching solutions to one-dimensional variational problems. World Scientific, 2001.
3. A. O. Ivanov, D. P. Ilyutko, G. V. Nosovsky, A. A. Tuzhilin, A. T. Fomenko. Computer Geometry: A Practicum. Moscow, 2010, 391 pp.; 2nd ed., URSS, 2024, 384 pp.

Selected papers

1. A. O. Ivanov, I. M. Nikonov, A. A. Tuzhilin. Sets admitting connection by graphs of finite length. Sbornik: Mathematics, 196:6 (2005), pp. 845–884.
2. A. O. Ivanov, A. A. Tuzhilin. Minimal fillings of finite metric spaces and convex polyhedra. arXiv:2607.27211 [math.MG] (2026).
3. A. Ivanov, G. Nosovskiy, A. Chekunov, D. Fedoseev, V. Kibkalo, M. Nikulin, P. Popelensky, S. Komkov, I. Mazurenko, A. Petiushko. Manifold hypothesis in data analysis: double geometrically-probabilistic approach to manifold dimension estimation. arXiv:2107.03903 [cs.LG; stat.ML].
4. A. O. Ivanov, G. V. Nosovskiy, V. A. Kibkalo, M. A. Nikulin, F. Yu. Popelensky, D. A. Fedoseev, I. V. Gribushin, V. V. Zlobin, S. S. Kuzin, I. L. Mazurenko. Recognition of anomalies of a previously unknown type. Chebyshevskii Sbornik, 23:5 (2022), pp. 227–240.

More than 150 scientific works, including monographs and textbooks (jointly with colleagues), have been published by A. O. Ivanov. The full list of publications (229 records) is given on the Full list of publications page.

5. Links and sources

• Russian personal page: dfgm.math.msu.su/people/ivanov/.
• ISTINA profile: istina.msu.ru.

Compiled from the department page dfgm.math.msu.su/people/ivanov/ (biography, research interests, teaching, publications).