Zoltán Füredi

Zoltán Füredi
Name	Zoltán Füredi
Birth date	1949
Birth place	Hungary
Fields	Combinatorics, Discrete Geometry
Workplaces	Alfréd Rényi Institute of Mathematics, University of Szeged
Alma mater	Eötvös Loránd University
Doctoral advisor	Pál Erdős

Zoltán Füredi is a Hungarian mathematician known for contributions to combinatorics, extremal graph theory, and discrete geometry. He has held positions at major Hungarian institutions and collaborated with leading figures in graph theory and combinatorics such as Paul Erdős, János Pach, and Miklós Simonovits. His work includes sharp bounds in extremal problems, constructions in hypergraph theory, and results linking combinatorial geometry with probabilistic methods.

Early life and education

Füredi was born in Hungary and completed undergraduate and graduate studies at Eötvös Loránd University in Budapest, where he worked in circles connected to the Alfréd Rényi Institute of Mathematics and met figures from the Hungarian school including Paul Erdős and János Komlós. He obtained his Ph.D. under the supervision of Pál Erdős and developed early research ties with researchers at the Hungarian Academy of Sciences and the Loránd Eötvös Mathematical Society.

Academic career and positions

Füredi has been affiliated with the Alfréd Rényi Institute of Mathematics and the University of Szeged and has held visiting appointments at institutions like Princeton University, Massachusetts Institute of Technology, and the Institute for Advanced Study. He collaborated with international groups at conferences organized by bodies such as the European Mathematical Society, the American Mathematical Society, and the International Congress of Mathematicians. He served on editorial boards for journals connected to Combinatorica, Journal of Combinatorial Theory, Series A, and other periodicals linked to Springer Science+Business Media and Elsevier.

Research contributions and major results

Füredi's research spans extremal combinatorics, hypergraph theory, and discrete geometry, producing results that have been cited across literature by authors like Paul Erdős, Miklós Simonovits, Béla Bollobás, Ronald Graham, and József Beck. He obtained sharp bounds for Turán-type problems related to the Turán theorem and worked on extremal numbers for forbidden subgraphs including cycles and complete bipartite graphs studied in contexts by Paul Turán and Erdős–Stone theorem discussions. Füredi provided constructions and asymptotic estimates in hypergraph matchings and coverings tied to problems studied by Edward R. Scheinerman and László Lovász.

In discrete geometry, he contributed to results on point sets, incidences, and unit distances connected to classical problems of Paul Erdős and the Sylvester–Gallai theorem, intersecting with work by János Pach and Miklós Székely. He applied probabilistic methods inspired by Alfréd Rényi and Noga Alon, and combinatorial techniques influenced by Erdős–Rényi model reasoning and Ramsey theory problems introduced by Frank P. Ramsey. Füredi's papers include extremal constructions using combinatorial designs related to investigations by Richard M. Wilson and Ronald L. Graham and algebraic methods that resonate with work by Noga Alon and Van H. Vu.

His studies on matchings in uniform hypergraphs and bounds for chromatic numbers of Kneser-type hypergraphs connect to literature by Lovász, Hubert Bray, and contributors to the Erdős–Ko–Rado theorem circle. Füredi also explored combinatorial set systems, intersecting with results by Erdős–Ko–Rado, and contributed to the development of techniques used in contemporary studies by Jacob Fox and David Conlon.

Awards and honors

Füredi has received recognition from Hungarian and international mathematical communities, including honors associated with the Hungarian Academy of Sciences and invitations to deliver plenary lectures at conferences organized by the European Mathematical Society and the International Congress of Mathematicians satellite meetings. He has been cited in lists of prominent researchers in combinatorics alongside figures such as Paul Erdős, Béla Bollobás, and Imre Csiszár.

Selected publications

- "Extremal problems for directed graphs" — appeared in journals frequented by researchers like Béla Bollobás and Paul Erdős discussing themes related to Turán theorem variants. - "The maximum number of unit distances in a convex polygon" — contributing to the Erdős unit distance problem discourse shared with János Pach and Péter Frankl. - Papers on hypergraph matchings and coverings that build on frameworks used by László Lovász and Richard Stanley. - Works on set systems and intersecting families with links to the Erdős–Ko–Rado theorem literature and the studies of Frankl.

Influence and legacy in combinatorics

Füredi's contributions are embedded in the development of modern extremal combinatorics and discrete geometry, influencing research by scholars such as Noga Alon, János Pach, Miklós Simonovits, Béla Bollobás, and successive generations working on Turán-type problems, hypergraph theory, and incidence geometry. His techniques are taught in graduate courses at institutions like Eötvös Loránd University, University of Szeged, and referenced in monographs by Béla Bollobás and László Lovász. The problems he posed and the bounds he proved continue to appear in open problem lists circulated by the American Mathematical Society and in programmatic research agendas at institutes such as the Institute for Advanced Study and the Alfréd Rényi Institute of Mathematics.

Category:Hungarian mathematicians Category:Combinatorialists