János Pach

Research Pach has authored several books and over 300 research papers. He was one of the most frequent collaborators of Paul Erdős, authoring over 20 papers with him and thus has an Erdős number of one.

Pach's research is focused in the areas of combinatorics and discrete geometry. In 1981, he solved Ulam's problem, showing that there exists no universal planar graph. In the early 90s together with Micha Perles, he initiated the systematic study of extremal problems on topological and geometric graphs.

Some of Pach's most-cited research work concerns the combinatorial complexity of families of curves in the plane and their applications to motion planning problems the maximum number of k-sets and halving lines that a planar point set may have, crossing numbers of graphs, embedding of planar graphs onto fixed sets of points, and lower bounds for epsilon-nets.

Awards and honors Pach received the Grünwald Medal of the János Bolyai Mathematical Society (1982), the Lester R. Ford Award from the Mathematical Association of America (1990), and the Alfréd Rényi Prize from the Hungarian Academy of Sciences (1992). He was an Erdős Lecturer at Hebrew University of Jerusalem in 2005. In 2011 he was listed as a fellow of the Association for Computing Machinery for his research in computational geometry. In 2014 he was elected as a member of Academia Europaea, In 2022 he was elected corresponding member of the Hungarian Academy of Sciences.

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