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Principal Lecturer János Pach
Subject Geometric Graph Theory
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May 28  June 1, 2002 Gateway Center
University of North Texas, Denton
Principal Lecturer
János Pach is Professor of Computer Science at City
College (CUNY), Research Professor at the Courant Institute (NYU)
and at the Rényi Institute (Hungarian Academy of Sciences).
He has published the monograph
Combinatorial Geometry (with P. K. Agarwal, Wiley, 1995)
and about 150 research papers. He serves on the editorial
boards of five technical journals and is a recipient of
the Lester Ford Award (Mathematical Assocation of America,
1990), the Rényi Award (1993) and the Academy Award
(Hungarian Academy of Sciences, 1998).
Among other results, Professor Pach
 settled Ulam's problem by showing that there exist no universal
countable graphs (1981);
 together with Bárány and Füredi verified L. Fejes
Tóth's Six Circle Conjecture, stating that in any
6neighbored circle packing in the plane either all
circles are of the same size, or there are arbitrarily
small circles (1984);
 together with de Fraysseix and Pollack discovered the first
efficient algorithm for drawing a planar graph using straight
line edges on a linear sized grid, and thus solved a famous
open problem of Rosenstiehl and Tarjan (1990);
 together with Törocsik proved the conjecture of
Erdos, Hanani, and Perles, stating that for
every k
the number of edges of a geometric graph of
n vertices having no
k
pairwise disjoint edges is O(n)
(1994);
 proved that there is a constant
C_{d}
such that any
nelement sets
P_{1},
. . . ,
P_{d+1}
in general position in
dspace have
C_{d} nelement
subsets
Q_{1},
. . . ,
Q_{d+1}
such that all simplices
induced by picking one point from each
Q_{i}
have an interior point in common (1998);
 together with G. Tóth solved a 40 years old problem
of Benzer, Sinden, Graham, and Kratochvil, showing that
the recognition of "string graphs" (i.e., intersection
graphs of plane Jordan curves) is decidable (2000).
Professor Pach has given many lectures on Geometric Graph
Theory, including a onehour plenary address at the Annual
Meeting of the American Mathematical Society (Atlanta, 1996)
and the Sixth Annual Charles H. Franke Memorial Lecture
(Seton Hall, 2000). He was a principal speaker at the
British Combinatorial Conference (Canterbury, 1999). The
text of this latter lecture, published in the London
Mathematical Society Lecture Note Series, is the most
comprehensive survey of Geometric Graph Theory.
