To represent a graph in geometric way is a very natural and old problem. For example, it was proved by Steinitz early in this century that every 3-connected planar graph can be represented as the graph of vertices and edges of a (3-dimensional) polytope.
In these talks we discuss a variety of old and new results connected with such representations. We describe very special Steinitz representations by Koebe, Andre'ev and Thurston, and show how these are related to to a spectral invariant introduced by Colin de Verdière in more than one way. We also show applications to the stability of "tensegrity frameworks".
The real challenging open questions start in the next dimension. Here the role of planar graphs is played by those graphs linklessly embeddable in 3-space. Some of the connections mentioned above have been extended: for example, these graphs can be characterized through the Colin de Verdière number. Others are conjectured or only suspected.
László Lovász held the Chair of Geometry at the University of Szeged from 1975-1982 and the Chair of Computer Science at the Eötvös Loránd University in Budapest from 1983 to 1993. He was A.D.White Professor-at-Large at Cornell University from 1982 to 1987. He is a member of the Hungarian Academy of Sciences and three other Academies.
His awards include the George Pólya Prize of the Society for Industrial and Applied Mathematics (1979), the Ray D. Fulkerson Prize of the American Mathematical Society and the Mathematical Programming Society (1982), the Brouwer Medal of the Dutch Mathematical Society (1993), and the Wolf Prize (Israel, 1999). He is editor-in-chief of Combinatorica and editor of 12 other Journals.
His field of research is discrete mathematics, in particular its applications in the theory of algorithms and the theory of computing. He has written 4 research monographs and 3 textbooks, and about 200 research papers.
For information about accomodation, see the program for the XXVth Ohio State-Denison Mathematics Conference, May 18-21.