With Füredi he proved that no deterministic polynomial time algorithm determines the volume of convex bodies in dimension d within a multiplicative error dd.
With Füredi and János Pach he proved the following six circle conjecture of László Fejes Tóth: if in a planar circle packing each circle is tangent to at least 6 other circles, then either it is the hexagonal system of circles with identical radii, or there are circles with arbitrarily small radius.
He is an editor-in-chief for the journal Combinatorica,[8] and an Editorial Board member for Mathematika[9] and the Online Journal of Analytic Combinatorics".[10]He is area editor of the journal Mathematics of Operations Research.[11]
References
^ a b c d e"DBLP Bibliography". Universitat Trier. Retrieved 29 January 2010.
^J. J. Sylvester, Problem 1491. The Educational Times, April, 1864, London
^Bárány, Imre,Sylvester's question: the probability that n points are in convex position. Annals of Probability, vol. 27 (1999), no. 4, pp. 2020–2034