#### Department of Mathematics

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2000 Zassenhaus Lectures

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László Lovász

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Microsoft Research, Redmond, Washington

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May 18th, 4.30pm-5.30pm, UH014

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May 19th, 4.30pm-5.30pm, MP1000

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Graphs, spectra and Steinitz
representations

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.

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Biography

Candidate of Math. Sci., Hungarian Academy of Sciences, Budapest, Hungary, 1970
Ph.D., (Mathematics), Eötvös Loránd University, Budapest, Hungary, 1971
Ph.D., (Mathematical Sciences), Hungarian Academy of Sciences, 1977
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.