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INTERNATIONAL AND DOMESTIC LINKS OF THE DEPARTMENT
Here you can find information about our scientific relations with foreign and Russian universities, research centers, well-known mathematical communities and outstanding mathematicians. Joint scientific programs, participation in some conferences and schools are listed. Our employees, graduate students and students repeatedly go on business trips for various periods of time. In turn, famous foreign scientists come to our department. Some photographs of their reports are posted on our website. Below we also indicate where some of our graduates work. Countries and cities mentioned are listed alphabetically: AUSTRALIA, AUSTRIA, ENGLAND, BRAZIL, VIETNAM, GERMANY, HOLLAND, GREECE, EGYPT, IRAN, ITALY, CANADA, CHINA, POLAND, SERBIA, SINGAPORE, USA, FRANCE, SWITZERLAND, JAPAN. CIS countries: AZERBAIJAN, BELARUS, KAZAKHSTAN, TAJIKISTAN, UKRAINE. In Russia: VOLGOGRAD, VORONEZH, KAZAN, NOVOSIBIRSK, PETERSBURG, CHELYABINSK, YAROSLAVL.This account is brief. We do not pretend to provide a complete overview of our many scientific contacts. This section was written in October 2012. Details can be obtained from the department staff (room 475 on the 4th floor of the Second Building and room 16-19 on the 16th floor of the main building).
AUSTRALIA AUSTRIA
The laboratory brought together specialists from leading scientific centers in Austria (IST), Russia (MIAN, MSU, YarSU, MIPT, IPPI, St. Petersburg State University), USA (University of Texas, Brownsville). Although the collaboration began recently, there are already new theoretical and applied results obtained through joint discussions and research within the project. Also, as part of the work of the Delaunay Laboratory, employees and graduate students of our department give lectures and conduct classes with Yaroslavl students. They participated in the Summer School on Discrete Geometry and Topology near Yaroslavl, as well as in organizing and conducting several international conferences, such as Conference on Discrete Geometry and Algebraic Combinatorics (April 23-27, 2012, Brownsville, TX, USA), International Topological Conference “Alexandrov Readings” (May 21-25 2012, Moscow State University), Yaroslavl international conference “Discrete Geometry” dedicated to the 100th anniversary of A.D. Aleksandrova(August 13-18, 2012, YarSU), see photo-1a. Participation in the work of the Delaunay Laboratory not only strengthens the international scientific connections of the department, but also contributes to the development of interest in new topical problems of modern discrete and computational geometry and topology. It should be noted the cooperation of A.T. Fomenko and his students (since 1996) with the Technical University of Vienna, in particular with: Institut für Analysis, Technische Mathematik und Versicherungsmathematik. There was an active joint program in the field of Riemannian geometry with the team of Professor Peter M. Gruber.
ENGLAND For many years, A.T. Fomenko has been publishing in England, at the Cambridge Scientific Publishers, a series of scientific monographs: Reviews in Mathematics and Mathematical Physics, where research by both domestic and foreign mathematicians and physicists is published. Among them, for example, are the following works: A.V.Pogorelov - “Multidimensional Monge–Ampère Equation”, E.I.Moiseev, A.V.Prudnikov, A.M.Sedletskii - “Basis Properties and Completeness of Certain Systems of Elementary Functions”, I.V.Mykytyuk - “Invariant Kähler Structures on the Cotangent Bundle of Symmetric Spaces and Reduction”, D.B.Zotev - “Topology of Integrable Systems: the Fomenko Theory”, and many others. BRAZIL
In May-June 2002 and May-June 2012, our department was visited by Professor of the University of Sao Paulo (Brazil) Dasiberg L. Gonsalves. He took part in the international conference “Alexandrov Readings” (2002 and 2012), worked with S.A. Bogaty, H. Zieschang and E.A. Kudryavtseva on intersection and coincidence problems, implementation of branched coverings between surfaces, quadratic equations in free groups, etc. He also gave presentations on Nielsen’s theory in the coincidence problem. In November-December 2003, E.A. Kudryavtseva went to the University of Sao Paulo (Brazil) to work with Professor D.L. Gonsalves, participate in a topological conference in San Carlos (December 2003, report on the Weken property in the problem of roots for mappings between surfaces). Published 8 joint articles by D.L. Gonsalves and E.A. Kudryavtseva, in collaboration with H. Zieschang and S.A. Bogaty. Currently, joint work continues on the problem of implementing indecomposable branched coverings between surfaces. In 2010, Professor D. Gonsalves, see photo-7, photo-8, invited A.A. Tuzhilin to give a minicourse at the University of Sao Paulo (USP). The topic of the course was computational geometry and optimization. A.A. Tuzhilin reviewed the main problems within the designated topic and demonstrated how classical and modern problems in this area can be studied and illustrated using the Mathematica package developed by the Wolfram Group. At the same time, a popular introduction to the Mathematica package was given, so that students had the opportunity to quickly engage in creative experimentation on their own.
VIETNAM
GERMANY
One of the striking results of the deep scientific contacts of our department in the field of modern geometry with foreign scientific centers was joint research with a group of German scientists (University of Bremen), headed by Peter Richter. At the invitation of the University of Bremen, A.T. Fomenko and A.V. Bolsinov gave a course of lectures on the foundations of the theory of topological classification of integrable systems created by A.T. Fomenko, his students and colleagues. One of the most important applications of the theory is the calculation of invariants of specific dynamic systems known in physics, mechanics, geometry. Such calculation often uses ideas and methods from computer geometry. As a result of fruitful collaboration with a group of German scientists led by Peter H. Richter. This group then included, in particular, the mathematicians Dullin and Wittek. As a result, it was possible to obtain a complete description of the topology of Liouville foliations for a series of dynamical systems, united under the name “Kovalevskaya case”. See article: A.V.Bolsinov, P.Richter, A.T.Fomenko. The method of circular molecules and the topology of Kovalevskaya's top. - Mathematical Collection, 2000, volume 191, No.2, pp. 3-42. The results turned out to be so interesting and unexpected that a computer film “Kovalevskaya Top” (“Kovalevskaya Top”) was made in Germany, in which it was possible to visually present the various modes of rotation of the “Kovalevskaya top”, the resulting bifurcations of Liouville tori, and also demonstrate “atoms” and “molecules”, that is, discrete Fomenko-Zieschang invariants that classify integrable systems with topological accuracy equivalence. For many years, our department has been participating in the Euler scientific and educational program for the exchange of students and staff with the German University in Bochum. Every year, several of our undergraduates, graduate students and staff travel to Germany for various periods of time (several weeks or months). The program was initially led by Professor Heiner Zieschang, a renowned mathematician and, in particular, an outstanding specialist in the field of three-dimensional topology. For a long time he collaborated with our department. Together with A.T. Fomenko, several important mathematical works were written in the field of topological invariants of three-dimensional graph-manifolds and integrable differential equations. This is how the well-known Fomenko-Zieschang invariant appeared, which classifies integrable systems with two degrees of freedom up to Liouville equivalence. Heiner Zieschang was a professor at the Ruhr University in Bochum (Germany), an honorary doctor of the University of Toulouse (1996) and an honorary professor at Moscow State University (1997). Currently, the Euler program is led by Professor H. Flenner in Bochum and Academician A.T. Fomenko at the Faculty of Mechanics and Mathematics of Moscow State University. At our department, the Euler program is also led by Associate Professor E.A. Kudryavtseva. As part of the Euler program, employees of the Ruhr University in Bochum (Germany) came to our department - Professor Heiner Zieschang (1997, 1998), Professor Uwe Abresch (3 weeks in 2003, special course “Yamabi equations on Riemannian manifolds”, report “On the topology of Riemannian manifolds of bounded curvature”), Professor Hubert Flenner (3 weeks in April 2004). As part of the Euler program, members of our department went for 2 weeks to the Ruhr University in Bochum (Germany) with scientific reports - F.Yu.Popelensky (November 2001), A.A.Oshemkov (July 2002), A.A.Tuzhilin (2003), E.A.Kudryavtseva (July-August 2003), A.O. Ivanov (2003-2004), S.A. Bogaty. A.A. Tuzhilin visited Germany several times - at the end of 1993 - beginning of 1994, together with A.V. Bolsinov and V.V. Trofimov; then in 1996, 2002, 2006 and 2011.
As part of the Euler program, students and graduate students of the Faculty of Mechanics and Mathematics of Moscow State University (mainly our department, as well as the department of higher algebra and the department of general topology) received an Euler scholarship in Moscow for 9 months, attended free German language courses at the Russian-German Institute at Moscow State University and went to the Ruhr University in Bochum (Germany) for a month:
Participant of the Euler program 2001-2002 N.V. Korovina, at the invitation of Ruhr University, worked for 2 years as an assistant at the Ruhr University Bochum in the department of Professor Knieper (2003 - 2005). E.A. Kudryavtseva went on a 2-year internship (1999-2001) to the Ruhr University Bochum: the first year as part of the DAAD (German Academic Exchange Service) program, the second year - at the invitation of the Ruhr University she worked as an assistant at the Ruhr University Bochum in the department of Professor H. Zieschang. She worked with Professor H. Zieschang and his visitors (from Brazil, France, China, Russia, Ukraine) in the areas of low-dimensional topology, coincidence theory and Nielsen theory, equations in free groups. She gave 17 reports at the universities of Bochum, Frankfurt, Dortmund, Freiburg on her (as well as joint with H. Zieschang and others) results. Among other things, she made presentations at the International Conferences on Low-Dimensional Topology in Frankfurt (June 2000) and Oberwolfach (October 2000, report “Nielsen root numbers of mapping between surfaces”). I.M. Nikonov has repeatedly given presentations at German universities and institutes: Bochum (2002, 2006), Bielefeld (2006), Oberwolfach (2012). In the 2000-2001 academic year, a unique research seminar on invariants of knots and magnetic fields was held at the Ruhr University of Bochum - a joint seminar of the topological group of Professor H. Zieschang (Faculty of Mathematics) and the group of Professor G. Hornig (Department of Theoretical Physics-VI Faculty of Physics). This cooperation turned out to be fruitful: later E.A. Kudryavtseva visited Professor G. Hornig in July-August 2003, and G. Hornig and his graduate student H. Von Bodecker visited our department in January 2002. Professor H. Zieschang came to our department for 2 years (2001-2003) for scientific and teaching work within the framework of the “Stiftungsinitiative Johann Gottfried Herder” program. He gave special courses on “3-dimensional manifolds”, “Seifert manifolds”, “Fixed points and coincidence points”. In Moscow, Professor H. Zieschang continued to work together with A.T. Fomenko, S.A. Bogaty, E.A. Kudryavtseva and D.L. Gonçalves (Sao Paulo, Brazil) on the coincidence problem, quadratic equations in free groups, and the problem of realizing ramified coverings between surfaces. In total, H. Zishang and E. A. Kudryavtseva published 13 joint articles (some in co-authorship with S. A. Bogaty, O. V. Bogopolsky, R. Weidmann, S. Wang, D. L. Gonsalves and K. Hayat). In February-March 2012, the Russian-German conference on multidimensional complex analysis was held at the V.A. Steklov Mathematical Institute in Moscow. Many of the German participants are employees of the Ruhr University Bochum. One of the invited speakers was E.A. Kudryavtseva (report “Integrable Hamiltonian systems with incomplete flows and Newton polygons”) For many years, our department has been associated with the famous Max Planck Institute for Mathematics in Bonn; our employees have repeatedly visited there for joint research and participated in many conferences organized by the institute. For example, at the seminar of Yu.I. Manin, see photo 17, who for a long time was one of the directors of the Max Planck Institute, algebraic-geometric problems of integrable dynamic systems of differential equations and the theory of bifurcations in Liouville foliations were discussed. An active discussion of problems in the multidimensional calculus of variations took place at the seminars of Professor S. Hildebrand. In 1996, A.O. Ivanov and A.A. Tuzhilin were invited by Professor S. Hildebrant to the University of Bonn for joint creative work. The result was a work that describes the amazing properties of polygons that are close to regular. In addition, during the joint report of Ivanov and Tuzhilin, Professor S. Hildebrandt asked the question: is it true that for generic boundaries the minimal Steiner trees connecting them are unique? A few years later, Ivanov and Tuzhilin gave a positive answer. Subsequently, K.I. Oblakov, a student of Professor S.A. Bogaty from the Department of General Topology, significantly generalized the result of Ivanov and Tuzhilin. Photo 18 shows Ivanov and Tuzhilin at the 1994 International Mathematical Congress in Zurich.
In 1998, A. Ivanov and A. Tuzhilin worked for several months at the Max Planck Institute for Applied Mathematics (Leipzig) in the department of Professor Jorgrn Jost, a well-known specialist in multidimensional geometric variational problems. A. Ivanov and A. Tuzhilin were engaged in joint scientific research there with Prof. Hong Van Le, a well-known specialist in multidimensional minimal surfaces (Hong Van Le is a graduate of our department, doctoral student A.T. Fomenko). As a result of this collaboration, new results were obtained on the geometry of branched extremals of Lagrangian-type functionals and on stability conditions for locally minimal networks on the Manhattan plane. At the mathematical congress in Berlin in 1998, A. Ivanov and A. Tuzhilin met Dietmar Cieslic, a well-known specialist in the geometry of shortest trees, the Steiner relation and applied issues of the theory of optimal connections. Dietmar Cislik, see photo 19, is an employee of the University of Greifswald (Ernst-Moritz-Arndt-Universitat Greifswald), one of the oldest universities in Germany. From 1999 to 2003, A. Ivanov and A. Tuzhilin repeatedly visited Greifswald for joint scientific work, as a result of which new results were obtained on shortest trees in phylogenetic spaces, as well as on the Steiner relation of Riemannian manifolds.
Since 1999, a group led by Professor J. Brüning has been working at Humboldt University as part of the DFG project. The activities of this team include, in particular, problems of geometric and semiclassical quantization, geometry and spectral properties of singular spaces, the theory of differential equations on graphs and other cellular complexes. In 2000–2002, members of this group invited professor of our department A.I. to Berlin for joint scientific work. Shafarevich. As a result, a number of works appeared devoted to the quantization of singular manifolds, as well as geodesic flows, demonstrating both integrable and chaotic behavior of trajectories. In addition, a graduate of our department S.E. defended her dissertation at Humboldt University. Roganova, student of A.I. Shafarevich and J. Bruning. To the Rhine University Bonn A.I. Shafarevich was repeatedly invited to work together with a group led by Professor S. Albeverio. A number of works have been published on nonlinear hydrodynamic equations and connections between their solutions and topological invariants of vector fields. In 2002, A.I. Shafarevich was invited to the Technical University of Cottbus to give a semester-long course of lectures for employees, graduate students and senior students on the topological and asymptotic properties of hydrodynamic equations, as well as for joint scientific work. In 2002, a research group was created at the Humboldt University of Berlin under the leadership of Professor H. Kurke, where a member of the department A.B. Zheglov worked for several years (2002-2006) on a project to develop the multidimensional theory of the KP equation. As a result, a number of joint publications appeared, in 2005 an international conference was organized and held in Berlin, and a large number of reports were made at seminars and conferences in different cities of Russia and Europe. Work on the project, as well as contacts with members of the scientific group, continues now: since 2006, the group has regularly conducted research at various mathematical institutes in Europe: the Oberwolfach Mathematical Institute in Germany, ICTP in Italy, ESI in Austria, see photo 20, photo 21. The last time Professor Kurke came to Moscow in May 2012 at the invitation of the department to continue joint research. It is worth noting that research on this topic was carried out by other famous scientists from Moscow, such as academician A.N. Parshin and D.V. Osipov from the Mathematical Institute. Steklov, with whom close contacts have been maintained for many years, and who, in turn, have deep connections with the Humboldt University of Berlin. New joint scientific research by A.B. Zheglov and Professor I. Burban from the University of Cologne is also closely related to this project.
Department staff regularly participate in conferences held by Mathematisches Forschungsinstitut Oberwolfach. Thus, at a conference in 2008, one of the four organizers was V.O. Manturov, and in 2012 at the conference “Invariants in Low-Dimensional Topology and Knot Theory” D.P. Ilyutko, I.M. Nikonov made reports, and our graduate student D.A. Fedoseev also took part. The proceedings of the 2008 conference were published in three special issues of the “Journal of Knot Theory and Its Ramifications”, in which V.O. Manturov, D.P. Ilyutko and a graduate student of the department D.M. Afanasyev published their works. 2008 was declared the year of mathematics in Germany. In this regard, a large number of mathematical seminars and courses in various areas were organized in Germany. Among them was a semester on knot theory, organized by the Mathematical Center in Heidelberg. Our department was represented at this seminar by D.P. Ilyutko and V.O. Manturov, where they made presentations, and V.O. Manturov also gave lectures on the theory of knots. All these scientific connections of the department allowed some graduates of our department to get permanent jobs in Germany. Among them, for example, are students of A.T. Fomenko - Prof. V.S. Matveev, see photo 22, E.N. Selivanova, N.V. Korovina. Professor V.S. Matveev became a famous scientist, his research on Riemannian geometry and Hamiltonian systems became widely known. He works at the University of Jena and maintains contacts with the Faculty of Mechanics and Mathematics of Moscow State University; some of our graduate students come to him for internships (for example, students of A.T. Fomenko - A. Fedorova and D. Tonkonog).
Today our department is closely connected with universities and mathematical institutes in the cities of Berlin, Bonn, Bochum, Heidelberg, Jena, Oberwolfach, Bielefeld. For example, photo 23 shows participants at the conference on knot theory in Oberwolvach in June 2012. Among the participants are V.O. Manturov, student of A.T. Fomenko (Manturov is standing in the second row), I.M. Nikonov and our graduate student D.A. Fedoseev, student of A.T. Fomenko (Nikonov and Fedoseev are sitting in the first row, in the center), D.P. Ilyutko (standing in the third row). Photo 24 shows participants of the conference in Heidelberg in 2008 (D.P. Ilyutko and V.O. Manturov are in the first row on the left).
HOLLAND
GREECE
EGYPT IRAN
In 2004, the University of Tabriz in Iran organized a special Iranian-Russian mathematical conference aimed at cooperation between our department and Iranian scientists. The city of Tabriz is the capital of one of the northern provinces of Iran. Employees of our department - professors A.V. Bolsinov and A.A. Oshemkov (students of A.T. Fomenko) were invited to this conference with the main plenary presentations on symplectic topology and the theory of integrable systems, see photo-28. Photos 29 and 30 show some of the meetings of our employees with mathematicians at this conference.
Iranian mathematicians who defended their dissertations at our department develop these studies at their universities in Iran and maintain scientific contacts with the department. ITALY Members of the department participated several times - in 1994, 2001-2004 and 2009 - in conferences and summer schools at the famous Abdus Salam International Center for Theoretical Physics (ICTP) in Trieste, Italy. For example, in 1994 it was a school on the geometry of differential equations. The ICTP Center is an international scientific organization under UNESCO. Every year, this institute hosts numerous scientific events designed to attract students, graduate students and young scientists from developing countries to participate in international scientific life. Our employees participated in the work and spoke at various conferences held in this center, primarily at schools on topology (2001) and non-commutative geometry (2004). In 2009, a school and conference on knot theory and its applications in physics and biology was organized at the Abdus Salam International Center for Theoretical Physics (ICTP). The staff of our department took an active part in the work of the school and the conference. V.O. Manturov was invited as a plenary speaker and gave a mini-course on the theory of knots at the school, D.P. Ilyutko, I.M. Nikonov and graduate student D.M. Afanasyev (student of A.T. Fomenko) made presentations. Thanks to this participation, the department developed contacts with Italian mathematicians, such as Renzo Ricca. Based on the results of this school-conference, works were published in which the department was represented by D.P. Ilyutko and V.O. Manturov. Photo 31 shows D.P. Ilyutko at a conference in Pisa.
In 2011, the European Science Foundation was organized at the Center for Mathematical Research named after. Ennio De Giorgia, Pisa, international school and conference on knot theory, which lasted two and a half months. Thanks to the successful participation of the staff of our department in the conference in Trieste, D.P. Ilyutko and V.O. Manturov were invited as lecturers to the school “Knots and gears: from theory to application”, and D.P. Ilyutko, V.O. Manturov and I.M. Nikonov as speakers at the conference “Knots and gears: from forms to functions”. CANADA
Queens University employs Professor O.I. Bogoyavlensky, a graduate of the Faculty of Mechanics and Mathematics of Moscow State University, a well-known specialist in the theory of integrable systems and mathematical physics. He maintains close contacts with our department and participates in joint scientific projects. His students interact with graduates of our department in the field of symplectic geometry and topology. In August 2001, E.A. Kudryavtseva participated in the International Conference “New techniques in topological quantum field theory” in Calgary (Canada), where she made a report “On the homotopy type of the space of Morse functions on surfaces.” In May 2004 and May 2012, Professor Peter Zvengrovsky from the University of Calgary (Canada) visited our department, he made several reports on spines of manifolds, etc. In 2004-2006 E.A. Kudryavtseva completed a 2-year internship at the University of Calgary (Canada) within the framework of the PIMS Visiting Research Fellowship program, where she worked at the department of topology with Peter Zvengrovsky and his colleagues on the Riemann zeta function (together with P. Zvengrovsky and F. Sajdak), K-theory (co-authored with P. Zvengrovsky and K.Varadarajan). She taught the scientific seminar “Noncommutative Geometry” and seminar classes on the course of mathematical analysis. She took part in the International Conference on Braid Groups and Their Applications in Banff (Banff International Research Station, report on topological invariants of magnetic fields), the 5-day conference “Homotopy Theory and Actions of Groups” in Banff (report “Degrees of Maps between Seifert Manifolds with a Finite Fundamental Group”), Winter Conference of the Canadian Mathematical Society 2005 (report “On Points”) coincidence of mappings of a torus into a surface"). She gave a colloquium report at the Faculty of Mathematics of the University of Calgary in 2006 on the topic “Relative periodic motions of planetary systems with satellites.” In addition to connections with Canadian topologists, the department has developed useful contacts with Canadian specialists in dynamical systems (in particular, integrable systems and celestial mechanics) - L. Bates (Calgary) and M. Santoprete (Waterloo). CHINA
In 1999-2000, E.A. Kudryavtseva and Professor of Peking University S. Wang (together with C. Hayat-Legrand and H. Zieschang), during their visit to the University of Bochum (Germany), obtained a result on the degrees of mappings between Seifert manifolds with a finite fundamental group. In June-July 2002, E.A. Kudryavtseva traveled to China (the cities of Beijing, Xi'an, Shanghai) with reports at the International Congress of Mathematicians (in Beijing) and at the Satellite Conference on Topology in Xian, with a report “On the Veken property in the problem of roots for mappings between surfaces.” In 2005, a group of employees from the Faculty of Mechanics and Mathematics of Moscow State University went on a study tour to Harbin Polytechnic University (HPU). The delegation from our department included A.O. Ivanov and A.A. Tuzhilin. Subsequently, cooperation agreements were concluded with a number of members of the delegation, as a result of which for the next three years A.A. Tuzhilin went every year for a couple of months to KhPU to teach differential geometry. On the initiative of A.A. Tuzhilin, the traditional teaching style adopted at Moscow State University was introduced at KhPU. Lomonosov and other Russian universities, including seminars, a verbal test and a verbal exam (usually there was no test, and the exam was written). Cooperation with KhPU continues to this day and is taking on new and more interesting forms. Employees and graduates of the department - I.M. Nikonov, F.Yu. Popelensky, G.I. Sharygin, V.O. Manturov - regularly take part in conferences on non-commutative geometry and algebraic topology held in China (Tianjin 2010, 2012, Harbin 2011). Department staff - I.M. Nikonov, F.Yu. Popelensky (students of Yu.P. Solovyov), G.I. Sharygin - regularly take part in conferences on non-commutative geometry held in China (Tianjin 2010, 2012, Harbin 2011). In 2012, a large group of undergraduate and graduate students of the Faculty of Mechanics and Mathematics, including students from our department (for example, Stanislav Nikolaenko), visited several leading universities in China. V.O. Manturov visited the Zhen Institute of Mathematics, Nankai University, Tianjin twice (July-August 2007, lecturing, scientific work, August 2011, scientific work). There are scientific contacts with Academician of the National Academy of Sciences of China Ge Molin. In 2012, V.O. Manturov visited the Center for Mathematical Sciences of Tsinghua University (Beijing) in September, the best university in China. At this university, V.O. Manturov gave a series of lectures (some of them in Chinese), and also founded a seminar on the theory of knots. V.O. Manturov constantly collaborates with university employee Van Han: there is one joint published article; Currently, work is underway to write lecture notes on V.O. Manturov’s mini-course (in Chinese). MEXICO POLAND The Polish Academy of Sciences constantly organizes conferences and schools on knot theory in Warsaw and Bedlewo. Our department was represented at these conferences by D.P. Ilyutko, V.O. Manturov and I.M. Nikonov. Thanks to these conferences, strong connections were established with such famous Polish mathematicians as B. Boyarski and P. Traczyk. Our employees also participated in conferences on algebraic topology and noncommutative geometry. In 2011, a summer school “Bi-Hamiltonian geometry and integrable systems” was organized at the Banach Center (Bedlevo), in which staff and graduate students of our department took an active part. One of the organizers and lecturers was A.V. Bolsinov, and among the listeners were our graduate students A.M. Izosimov, I.K. Kozlov, D.I. Tonkonog, who also made reports there. Employees of the department A.V. Bolsinov and A.I. Shafarevich repeatedly participated in the annual conference “Geometric Methods in Physics” held in Belovezhye. There are close connections with the University of Bialystok, in particular with its dean A.A. Odzhievich and professors A.V. working there. Lebedev and A.B. Antonevich SERBIA
In August 1995, E.A. Kudryavtseva was a member of the jury at the 7th summer session of the “Tournament of Cities” for schoolchildren, which took place in Novi Sad (Yugoslavia). In the international conference of 2012, entitled “17th Geometric Seminar”, employees and students of our department took an active part: Professor A.A. Tuzhilin gave a plenary report, and associate professors A.B. Zheglov (report “An analogue of the KP theory in dimension two”), D.P. Ilyutko (report “Extremal networks in normed planes and Maxwell formula”) gave invited presentations. E.A. Kudryavtseva (report “The topology of spaces of functions with prescribed singularities on surfaces”), F.Yu. Popelensky, G.I. Sharygin and students I. Kozlov (report “Elementary proof of Jordan-Kronecker theorem”) and S. Nikolaenko (report “Topology of the Liouville foliation in the integrable case of Goryachev in the problem of motion of a rigid body in fluid"). SINGAPORE
In 2005-2006, an employee of the Laboratory of Computer Methods in Natural Sciences and Humanities (at our department) G.V. Nosovsky received a Tan Chin Tuan Fellow grant, according to which he spent 3 months in Singapore at the Nanyang Technological University at the Faculty of Computer Science and Egineering for scientific work and lecturing on financial mathematics and computer geometry, see. photo-45 and photo-46.
The goal of the research group that arose at that time was to study the problem of clustering a cloud of points in Euclidean space based on proximity defined by Euclidean distance, identifying natural parameters that influence the result of clustering and creating a new clustering algorithm that would be devoid of the disadvantages of existing algorithms (for example, unstable recognition of clusters of non-convex shape). As a result, a new clustering method, ADACLUS, was developed, based on the influence function proposed by the group and on new statistics that effectively assess the deviation of intra-cluster density from uniform density. ADACLUS is capable of operating in fully automatic mode. In addition, a clustering algorithm using Delaunay triangulation was developed. It is characterized by high performance and is not inferior in clustering quality to most common algorithms, surpassing them in speed. Several articles have been published on this topic in high-ranking scientific journals, including the journal Pattern Recognition. These algorithms have already found application in applications of computer geometry to medicine, biology and satellite navigation, in modern computer geometry (pointwise graphics problems). In 2007, professor of our department A.A. Tuzhilin spent 2 months in Singapore at the Nanyang Technological University at the invitation of the University leadership to work together in the field of applications of differential geometry and Steiner network theory to biology, as well as to various engineering problems. All the tasks were successfully solved, and the algorithms created by A.A. Tuzhilin were implemented in the form of software. In 2009, G.V. Nosovsky spent 2 months in Singapore at the Nanyang Technological University for scientific work and participation in special seminars at the Faculty of Mechanical and Aerospace Engineering. Based on the results of scientific research carried out jointly with Professor V.V. Kulish in the field of stability of solutions to partial differential equations such as the heat equation with a fractional order of differentiation in time (used to model the processes of information transmission by neurons of the human brain) in relation to disturbances of this order, a scientific article was written. In addition, during this trip, G.V. Nosovsky and V.V. Kulish published a scientific article on financial mathematics, devoted to mathematical microanalysis of optimal economic behavior. In 2012, G.V. Nosovsky spent 2 weeks in Singapore at the Nanyang Technological University at the School of Electrical & Electronic Engineering to participate in the development of fast algorithms for providing a “power handle” - a new computer interface that allows the user to feel the forces that arise when moving a virtual object controlled by him, as well as when interacting with other objects in virtual space. This device is used, in particular, in various simulators that require practicing precise movements (for example, in surgery), as well as in molecular biology for the virtual synthesis of proteins. The development of its mathematical software, which works stably in real time, is one of the important areas of modern computer geometry. The department has extensive connections with the World Scientific publishing house, which is based in Singapore. One of the members of the editorial board of the Journal of Knot Theory and its Ramifications is V.O. Manturov. Staff, alumni, students and postgraduate students are regularly published by World Scientific and edit books published by this publishing house. D.P. Ilyutko, V.O. Manturov and D.M. Afanasyev published in the Journal of Knot Theory and its Ramifications; V.O. Manturov edited the book LinKnot, written by Serbian mathematicians S. Yablan and R. Sazdanovich. In the proceedings of the school-conference on the theory of knots, held in Trieste (Italy) in 2009, the works of D.P. Ilyutko and V.O. Manturov were published. In 2012, the book “Virtual Knot: The State of the Art”, written by V.O. Manturov and D.P. Ilyutko, was published. This book is part of the Series on Knots and Everything. USA
These contacts turned out to be useful in 2009, when creating a workshop on computer geometry at the Faculty of Mechanics and Mathematics of Moscow State University (A.A. Tuzhilin, A.O. Ivanov and other employees of the department). Of particular note is the long-term collaboration of our department with the outstanding American mathematician Alfred Gray (University of Maryland), who actively participated in computer geometric research at the Wolfram Center. Together with Alfred Gray, our department has carried out interesting work in the field of Riemannian geometry, topology and computer geometry. Thanks to this collaboration, Alfred Gray's famous book Tubes, dedicated to Riemannian geometry and topology, was published in Russian translation in Russia. A.T. Fomenko was also invited several times (1995, 1996, 1997) to the famous Dowling College (New York) to talk about the role of visual geometry and topology in the education of mathematicians. Our department also cooperates in the field of computer science and computer geometry with New York University (NYU), USA, where Alexey Tuzhilin’s cousin, Professor Alexander Tuzhilin, works, see photo 53.
In April 2011, D.P. Ilyutko visited one of the oldest universities in the USA, Dartmouth College. During his visit to the university, D.P. Ilyutko made a report at the faculty colloquium and seminar of the Faculty of Mathematics, see photo-54, photo-55. D.P. Ilyutko’s stay at Dartmouth College was initiated by the mathematics department and prof. V.V.Chernov. Thanks to this trip, close contacts were established with Dartmouth College professor V.V. Chernov.
Seminars of the Department of Differential Geometry and Applications were among the first in Moscow to regularly conduct remote reports via the Internet. Among the speakers were O. Ya. Viro (Stony Brook University, USA), L.H. Kaufman (University of Illinois at Chicago, USA). On the other hand, V.O. Manturov and I.M. Nikonov gave remote presentations at a conference at Stony Brook University, New York. Seminars of the Department of Differential Geometry and Applications (seminar “Knots and Representation Theory” and seminar “P.K. Rashevsky Seminar on Tensor and Vector Analysis with Applications to Geometry, Mechanics and Physics”) were among the first at MSU to begin practicing remote reports using the Skype system. Thus, many well-known mathematicians from abroad, mostly now working in the USA, spoke at the seminars (L.H. Kaufman, University of Illinois, Chicago, many times, Oleg Yanovich Viro, now working at the State University of New York at Stony Brook). Using Skype, V.O. Manturov and I.M. Nikonov made presentations at international conferences: June 2010 (Stony Brook, conference “Low-Dimensional Topology and Categorification”). Also in September 2010, V.O. Manturov gave a plenary report at the “Knot Theory and Its Ramifications” conference in Chicago. Our department has close ties with Professor Kaufman. He spoke several times at the department’s seminars (the seminar “Knots and Representation Theory” and the seminar “P.K. Rashevsky Seminar on Tensor and Vector Analysis with Applications to Geometry, Mechanics and Physics”) during his stay in Moscow. Collaboration with Professor Kaufman gave rise to collaboration with other American mathematicians, his students, H. Dai, A. Kaestner. The department staff also maintains close scientific contact with the University of Texas at Brownsville (Brownsville, TX, USA), see photo-56, photo-57, primarily with a group of specialists in discrete geometry, coding theory and packaging theory. Thus, members of our department regularly take part in the Conference of Discrete Geometry and Algebraic Combinatorics, held every two to three years on South Padre Island, near Brownsville, on the shores of the Gulf of Mexico, see photo 58. For example, in 2010, D.P. Ilyutko gave a report, and in 2012, Professors A.O. Ivanov and A.A. Tuzhilin, as well as our 1st year graduate student A.Yu. Eremin, gave presentations at this conference.
In 2012, an interesting tour of the university campus, which was built in the style of a colonial frontier fort, was organized for conference participants. We also managed to visit the computer modeling laboratories and the astrophysical laboratory that controls the world's largest radio telescope, located at Arecibo Observatory, Puerto Ric, see photo-59, photo-60. The tour of the Faculty of Mathematics was conducted by the Dean of the College of Science, Mathematics and Technology, Mikhail Bunyaev, see photo-61, and the head of the Department of Mathematics, Jerzy Mogilski. Currently, the leadership of the Faculty of Mechanics and Mathematics of the University of Texas is discussing the possibility of organizing joint master's programs under the “double degree” program, which is gaining momentum both in Europe and in America. Photo 62 shows famous mathematicians - Professor B. Conelli, who built the first example of a nested flexible polyhedron, and A. Berg - participants in the International Conference on Discrete Geometry and Coding Theory having lunch at a local restaurant on the pier.
FRANCE
Professor A.I. Shafarevich was repeatedly invited to Lyon for joint scientific work with employees of the Ecole Centrale de Lyon, see photo 64. As a result, close ties were established with Professor Jean-Pierre Loheac. A number of papers have been published on the spectral geometry of non-self-adjoint operators with applications to magnetohydrodynamics. In addition, the theory of generalized solutions of equations with discontinuous coefficients was developed; in particular, such solutions were studied for the system of magnetic induction equations. Cooperation is actively developing; in particular, Jean-Pierre Loeac comes to Moscow several times a year.
In 1999-2000, E.A. Kudryavtseva and professor of the University of Toulouse K. Hayat-Legrand (together with S. Wang and H. Zieschang), during their visit to the University of Bochum (Germany), obtained a result on the degrees of mappings between Seifert manifolds with a finite fundamental group. Professor Claude Hayat-Legrand from the University of Toulouse (France) came to our department in May 2003 and May-June 2012. to participate in the conference of the Russian-French Lyapunov Center at Moscow State University (2003) and in the International Conference “Alexandrovsky Readings” (2012). In September 2007, a conference “Braids, groups and varieties in Toulouse” was held in Toulouse, dedicated to the memory of Heiner Zieschang (emeritus professor at the University of Toulouse). At it, E.A. Kudryavtseva gave a plenary report “On the Weken property in the problem of roots on surfaces.” Students of our department D. Permyakov and I. Shnurnikov also participated. In August 2012, E.A. Kudryavtseva traveled to Toulouse at the invitation of the University of Toulouse to work together with professors C. Hiatt-Legrand and A. Legrand to study the topology of the space of Morse functions on surfaces. SWITZERLAND
At the Faculty of Mechanics and Mathematics of Moscow State University there is a large seminar led by professors T. Ratju, G. A. Chechkin, A. I. Shafarevich and S. S. Lemak, where problems of modern mechanics and geometry are studied. . Well-known foreign experts in the field of mechanics and geometry also speak at this seminar, for example, Professor Frederic Diaz, Secretary General of IUTAM - International Union of Theoretical and Applied Mechanics, see photo-68, photo-69, photo-70. In the spring and summer of 2012, T. Ratju gave a special course “Structures on Dirac manifolds” at Moscow State University, aimed mainly at undergraduate and graduate students of geometric studies. A significant group of students, graduate students and employees of the Department of Differential Geometry actively participates in the work of this seminar and the International Laboratory named after Daniel Bernoulli, see photo-71. This Laboratory includes representatives of several MSU teams as employees. The Department of Differential Geometry and Applications is represented by A.I. Shafarevich (group leader), A.A. Oshemkov, A.Yu. Konyaev, E.A. Kudryavtseva, A.B. Zheglov, A.M. Izosimov, graduate students and students I.K. Kozlov, D.A. Fedoseev, E.G. Puninsky, O.A. Zagryadsky, G.R. Zhukov, E.O. Kantonistova, S.S. Nikolaenko, G.E. Smirnov, D.I. Tonkonog, V.V. Fokicheva.
Along with this, there is another seminar led by prof. T. Ratju and prof. A.I.Shafarevich, where students, graduate students and staff of our department develop research on symplectic topology and geometry of integrable Hamiltonian systems. Several important works have already been published in the central press. Trips of students, graduate students and staff of our department are planned both to mathematical centers in Switzerland and to international conferences within the framework of this fundamental project. In October 2012, Prof. A.I. Shafarevich and graduate student I.K. Kozlov was invited by T. Ratju to work together at the Department of Geometric Analysis and at the EPFL International Bernoulli Center in Lausanne. Photo 72 shows a conference on geometry and quantization in China. Among the participants are T. Ratju, A.I. Shafarevich, A.B. Zheglov. In photo-73 - T. Ratju and A.I. Shafarevich at the conference on geometry and quantization in China.
JAPAN
Since 1993, at the University of Aizu, on the initiative of A.T. Fomenko and T.L. Kuniya, several scientific conferences of the joint project KDGIP-AIZU were held, to participate in which employees of the Department of Differential Geometry and Applications repeatedly went to Japan, see photo-79, photo-80, photo-81. These conferences were also attended by mathematicians and specialists in the field of computer geometry from Italy, France, Belgium, China, the USA, and Canada. Some of the most important results were presented at international congresses on computer geometry held in Italy and Belgium. One scientific conference within the framework of the KDGIP-AIZU project was held at Moscow State University, at the Faculty of Mechanics and Mathematics. A large group of specialists arrived from Japan and got acquainted with the latest achievements of the department in the field of computer geometry.
As one of the important results of the KDGIP-AIZU project, the book “Topological Modeling for Visualization” by A.T. Fomenko and T.L. Kuniya was written and published by the famous international publishing house Springer. It turned out to be a unique publication, since it was the first to “establish a bridge” between the topological aspects of modern geometry and topology, on the one hand, and computer experimental geometry, on the other. The book turned out to be in demand both by “pure” mathematicians and by specialists and engineers working in the field of computer science. As a member of the editorial board of the famous international journal on computer geometry - Virtual Reality - A.T. Fomenko actively contributes to the development of new methods of computer geometry. In 2001, contacts with Japanese researchers in the field of geometry and, in particular, computer geometry, were significantly expanded. A.T. Fomenko took a trip to Tokyo, to the famous Institute of Technology. The invitation came from the department where computer geometry methods are being developed. A.T. Fomenko was asked to talk about new geometric, topological and algorithmic methods developed at the Department of Differential Geometry and Applications. As a result, an agreement was concluded on joint research in the field of computer geometry. In particular, on the recommendation of A.T. Fomenko, several students of A.T. Fomenko, graduates of the department, were hired to work at the Tokyo Institute of Technology. For example, Olga Egorova, Irina Semenova and others. As a result, a group of specialists emerged who introduced new methods into computer geometry, developed, in particular, by the scientific school of A.T. Fomenko. Scientific contacts with the Tokyo Institute of Technology have successfully continued to this day. Recently, several more graduates of our department went there for permanent work. CIS countries: AZERBAIJAN, KAZAKHSTAN, TAJIKISTAN. Further, our employees give lectures on algebra, geometry and topology, conduct workshops on computer geometry, and teach students at the Moscow State University branch in Dushanbe. For example, under the guidance of prof. A.O.Ivanova, prof. A.A.Oshemkova and Assoc. D.P. Ilyutko defended 12 term papers here in 2012. Some students then enter the Faculty of Mechanics and Mathematics at Moscow State University. Photo-82 shows D.P. Ilyutko in Baku.
BELARUS UKRAINE In Russia: VOLGOGRAD
VORONEZH Many of our students and graduate students give scientific presentations at Voronezh winter schools, at the Mathematical Faculty of Voronezh State University, and at the Voronezh Institute of Mathematics. The exchange of scientific ideas, results, and publications has been established. KAZAN NOVOSIBIRSK Professor O.V. Bogopolsky (Novosibirsk), E.A. Kudryavtseva and H. Zieschang proved in 2002 an analogue of the Magnus theorem for fundamental groups of surfaces (for classes of simple curves on surfaces). In 2012, Professor A.E. Mironov (Novosibirsk Institute of Mathematics SB RAS) and A.B. Zheglov published a joint work. PETERSBURG In June 2002, the “Second International Russian-German Meeting on Geometry” took place, at which E.A. Kudryavtseva made a report on geometry. CHELYABINSK Then, developing methods of computer geometry, S.V. Matveev and A.T. Fomenko conducted extensive research and published in 1991 the book “Algorithmic and computer methods in three-dimensional topology". Due to the relevance of the topic, the book was quickly translated into English (Fomenko A.T., Matveev S.V. Algorithmical and Computer Methods in Three-Manifolds. - Kluwer Academic Publishers. The Netherlands, 1997) and gained great popularity among specialists in modern geometry. The cooperation between the scientific schools of S.V. Matveev and A.T. Fomenko has especially intensified in recent years. Their students exchange visits and inform each other of the latest achievements in the field of topology of integrable systems and the complexity of low-dimensional manifolds. In particular, a practice has developed for colleagues to mutually familiarize themselves with candidate and doctoral dissertations submitted for defense. Thus, today the cooperation of our two scientific schools is developing in the following directions.
YAROSLAVL
WHERE OUR GRADUATES WORK
THE DEPARTMENT POPULARIZES MODERN GEOMETRY AND TOPOLOGY IN SOCIETY For many years, our department has represented the Faculty of Mechanics and Mathematics of Moscow State University in the Consortium “Geometric Education in New Information Technologies” (president - Professor V.V. Pilyugin), which includes a number of largest technical universities, such as MEPhI University, technical universities MIREA, MAI, MATI on the one hand, and large companies engaged in computer and engineering development, such as Siemens PLM Software Company, ASCON, National Center of Computer Animation, Bournemouth University, INERTEK Company, etc. The goal of the Consortium is to unite the efforts of participants to develop education in all areas where computer geometry can be presented. The activities of the Consortium include both the development of new educational courses, and the organization and conduct of scientific seminars (the seminar “Computer Geometry and Applications” has been running for many years), the publication of the scientific online journal Computer Graphics and Geometry (http://cgg-journal.com/). In 2004, A.T. Fomenko made a big report at the international congress on education, which took place in Denmark, in Copenhagen. Problems and methods of geometry and topology occupy a significant place on the departmental website dfgm.math.msu.su, which is actively visited by students of the Faculty of Mechanics and Mathematics and plays a large role in the introduction of new ideas into the education system at the Faculty of Mechanics and Mathematics. In addition, our website contains many videos devoted to various issues of geometry and topology. In modern society, where the amount of information is almost limitless, scientific results have to compete for people’s attention along with opinions and judgments of often frankly empty content. Students of the Faculty of Mechanics and Mathematics are no exception in this case. In such a situation, popularizing scientific results, communicating them to the widest circle of listeners and readers, awakening interest and respect for science become primary tasks. The department pays close attention to these issues. For example, Professor A.T. Fomenko regularly gives popular lectures on geometry. These events are always popular and attract full audiences. The book “Visual Geometry and Topology” by Fomenko became a pass into the wonderful world of modern geometry. In 2012, a large (1 hour) documentary film Colors of Math was released (in Russian distribution the title sounds like “Sensuous Mathematics”), created by Ekaterina Eremenko, and dedicated to mathematics. Man has six senses, and the idea of the film is to show how these senses are refracted in such a seemingly abstract science, like mathematics. Six famous mathematicians - Cedric Vilani (Fields Medal winner in mathematics), Anatoly Fomenko (academician of the Russian Academy of Sciences), Aaditya V.Rangan, Gunter M.Ziegler, Jean-Michel Bismut, Maxim Kontsevich (Fields Medal winner), talk about their science and clearly explain its essence. For example, A.T. Fomenko’s story is dedicated to mathematics, “like sight.” E.V. Eremenko is a graduate of the Faculty of Mechanics and Mathematics of Moscow State University (1985), then studied at the directing department of VGIK, was a presenter and correspondent for television programs, created several interesting films. Works in Germany. All of her films received prizes at international film festivals and were shown on numerous television channels in Russia and abroad. The film “Colors of Math” was shown at the Moscow International Film Festival in 2012, attracted attention, and received numerous accolades from the press and television. See 5-minute trailer for this film on our website. Department assistant A.Yu. Konyaev conducts educational work on the Internet - until 2014, he headed the scientific section of the news publication Lenta.ru. Since 2015, he has been the editor-in-chief of the popular science online publication “N+1”. Here are some of the articles written by A.Yu. Konyaev, which interested many Internet visitors.
In conclusion, we present photographs of the staff of our department in 2012.
Fomenko Anatoly Timofeevich
n bodies such as a planetary system with satellites), magnetic fields, invariants of symplectomorphisms and magnetic fields. Integrable Hamiltonian systems – stable invariants of topological conjugacy, an analogue of Liouville’s theorem for systems with incomplete flows, connection with Newton’s polygons. Low-dimensional topology – minimizing the number of intersection and coincidence points (Nielsen theory) on surfaces, absolute degree of mappings, quadratic equations in free groups, subgroups of fundamental groups of surfaces, implementation of indecomposable ramified coverings between surfaces (Hurwitz problem). Singularities of smooth functions, parametric Morse theory (topology and stratification of spaces of functions with given singularities) on surfaces. Supervises undergraduate and graduate students.
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