International seminar  Geometry "in large", dedicated to 85 anniversary of A.V.Pogorelov (May 11-15, 2004, Kharkiv)

The International Seminar "Geometry " in the Large" dedicated to the memory of Academician Aleksei Vasiljevich Pogorelov was held from 11th to 15th May, 2004 in Kharkiv . The Seminar was arranged on the initiative of Department of Geometry (ILTPE) headed by A.V.Pogorelov from 1961 to 2000. Mathematical Department of ILTPE and Department of Geometry of Kharkiv National University took direct and active part in arranging, organizing and holding the Seminar.

The Seminar was opened on 11 th May at Kharkiv National University. The opening addresses were spoken by Prof. I.Zalyubovsky, Pro-rector of KhNU; Academician Dr.in Phys.-Math. E.Ya.Khruslov, Head of Mathematical Department of ILTPE; and Prof. Dr. in Phys.- Math. Yu.A.Aminov, Head of Deparment of Geometry at ILTPE. The speakers pointed out that the Seminar pursued three main objects: to pay tribute to Aleksei Vasiljevich, the outstanding mathematician, who had
set up a modern school of geometry in Kharkiv and whose  85th anniversary would be celebrated that year; to introduce mathematicians to new advances in the modern geometry " in the large" and to share ideas, methods and results as at any conference; and to introduce students and young scientists to a broad spectrum of promising lines of investigation and to inspire and stimulate interest in solving currently central geometrical problems.

The first report was given by V.A.Marchenko, Academician of NAS of Ukraine. It was dedicated to Aleksei Vasiljevich Pogorelov, his life and scientific research but the main points concerned a great deal of good, warm and sincere recollections
that were welcomed by the participants with great interest. Next was the speech by L.A.Pogorelov, the son of Aleksei Vasiljevich, who expressed his gratitude to the organizers of the Conference for their respect for the memory of A.V.Pogorelov.

The first day of the Seminar was concluded with the reports by Prof. I.Kh.Sabitov and Prof. V.I.Babenko. The former report entitled " Volumes of Polyhedra" reviewed the results on the recently solved "bellows" problem of the constancy of a flexible polyhedron volume under flexure. The latter report concerned some problems in the mechanics of thin elastic shells and their solutions in terms of the geometrical theory of thin shells derived by A.V.Pogorelov. In succeeding days presented were three 45-minute's reports each morning and three half an hour's reports each afternoon. The report by Prof. Yu.A.Aminov delt with the estimate of size of the Euclidean space region containing  the regular orthogonal Bianchi system with the families of coordinate surfaces  which were formed by pseudo-spherical surfaces. Prof. A.D.Milka  concerned  the linear flexures of starlike bipyramids and their application to the analysis of stability "model flexors". The report by Prof. D.D.Sokolov discussed the probabilistic approaches to studying pseudo-Riemannian manifolds of the general theory of relativity, and the report by Prof. V.I.Diskant  concerned the classical isoperimetric inequalities and their analogs, generalizations and refinements in the theory of mixed volumes. Of special interest was the report by Prof. J.D.Moore (Santa-Barbara, University of California) who told of new geometrical and topological methods of investigating  minimal submanifolds in Rimannian manifolds that had made possible the finding of a number of strong statements about the existence of minimal surfaces, homeomorphic to a sphere or a torus on a Riemannian manifold as a general case. Furthermore in the participants' memories retained were the speeches by Dr. A.L.Yampolski (extrinsical geometrical properties of vector fields as submanifolds of tangent bundle), Dr. A.I.Medyanik (Hadamard matrices and their geometrical applications), Dr. V.T.Lisitsa (manifolds with closed geodesics and related Hamiltonian systems), Dr. L.A.Masaltsev (isometric immersions  of Thurston geometries in the Euclidean space), Dr. S.I.Okrut (conformal submersions of Kahler  manifolds) et al. Moreover, young scientists, post-graduates and students participated actively in the Seminar with their interesting reports of original results. A total of 22 reports were presented.

It should be noted that within the limits of the Seminar a so-called "Internet-Conference" was held: a number of well-known geometricians having, for objective reasons, no way to take direct part in the Seminar gave review lectures dedicated to A.V.Pogorelov to their students. These are Corresponding Member of NASU Prof.  A.A.Borisenko (Valencia University, Spain), Prof. Yu.D.Burago (St.Peterburg University, Russia), Academician of AS of Brazil Prof.K.Tenenblat (Brasilia University, Brazil) et al.

In conclusion, shown was a TV film made by TV Company "Tonis" during the celebration of the 80 th anniversary of Academician A.V.Pogorelov  at the B.Verkin Institute for Low Temperature Physics and Engineering. In particular, the film included a half-an-hour's interview with Aleksei Vasiljevich that was very stirring and moving and left no one indifferent - neither former colleagues and students of A.V.Pogorelov that had worked with him many years and knew him well, nor numerous students which discovered for themselves, maybe for the first time, that Person and Scientist.

We hope that Seminar in Geometry in Kharkiv will be regular and, along with traditional geometrical conferences in Cherkassy, Abrau-Dyurso and Novosibirsk, will contribute to the maintenance of high prestige of Kharkiv Geometrical School, the
development and strengthening of its relations with important geometrical schools in Russia, USA, Poland and some other near and far foreign countries.

Seminar program and abstracts
Gallery of pictures