Abstract
The Yaroslavl International Conference on Discrete Geometry dedicated to the centenary of A. D. Alexandrov was organized by the International B.N. Delaunay Laboratory "Discrete and Computational Geometry" and took place from August 13 to 18, 2012 at the P.G. Demidov Yaroslavl State University. The purpose of this note is to highlight the main results presented at the conference and to discuss the role of the meeting in the development of the field of Discrete and Computational Geometry in Yaroslavl. The article is published in the author’s wording.
Highlights
Combinatorial Methods are of great importance in Discrete Geometry and Computational Topology
We feel it is important to underline the participation of many young mathematicians
Many of the talented young scientists attracted to the field of Discrete Geometry by the International Delaunay Laboratory presented their results at the conference
Summary
Discrete Geometry is a fast developing branch of modern mathematics, with applications in many areas, ranging from entertainment to manufacturing, and from medicine to facility planning. Alexandrov moved to the systematic study of convex polyhedra and surfaces He experienced a period of stormy activities and soon uncovered deep results on mixed volumes, defending his Doctoral Dissertation in the Spring of 1937. The method of solution was deep and surprising, being based on considerations of a similar problem about non-negative polyhedral metrics Along this way, Alexandrov discovered and proved one of the most amazing theorems in geometry, namely a criterion for an unfolding to be that of a convex polyhedron. Alexandrov found a way to recognize when a map of one manifold into another manifold is a map onto the entire second manifold By means of this method, he proved a series of results on the existence and uniqueness of polyhedra with given conditions. Alexandrov have been organized in major Russian centers of Discrete Geometry where his students are active: in Saint Petersburg, in Novosibirsk, and in Yaroslavl
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