János Pach

János Pach (born May 3, 1954)[2] is a mathematician and computer scientist working in the fields of combinatorics and discrete and computational geometry.

János Pach
János Pach at Graph Drawing 2009
Born (1954-05-03) May 3, 1954
Alma materEötvös Loránd University, Hungary, (M.S., Math., 1977; Ph.D., Math., 1981)
Hungarian Academy of Sciences, (Candidate, 1983; Doctorate, 1995) [1]
Occupationprofessor and mathematician
Known forcombinatorics and computational geometry


Pach was born and grew up in Hungary. He comes from a noted academic family: his father, Zsigmond Pál Pach was a well known historian, and his uncle Pál Turán was one of the best known Hungarian mathematicians.

Pach received his Candidate degree from the Hungarian Academy of Sciences, in 1983, where his advisor was Miklós Simonovits.[3]

Since 1977, he has been affiliated with the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences.[4]

He was Research Professor at the Courant Institute of Mathematical Sciences at NYU[5] (since 1986), Distinguished Professor of Computer Science at City College, CUNY (1992-2011), and Neilson Professor at Smith College (2008-2009).

In 2008, he joined École Polytechnique Fédérale de Lausanne[2] as Professor of Mathematics.

He was the program chair for the International Symposium on Graph Drawing in 2004 and Symposium on Computational Geometry in 2015. With Kenneth L. Clarkson and Günter Ziegler, he is co-editor-in-chief of the journal Discrete and Computational Geometry, and he serves on the editorial boards of several other journals including Combinatorica, SIAM Journal on Discrete Mathematics, Computational Geometry, Graphs and Combinatorics, Central European Journal of Mathematics, and Moscow Journal of Combinatorics and Number Theory.

He was an invited speaker at the Combinatorics session of the International Congress of Mathematicians, in Seoul, 2014.[6] also, He is an invited speaker at the 12th Winter School on Computational Geometry, in Tehran, Feb 2020.


Pach has authored several books and over 200 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.[7]

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.[8] In the early 90s[9] 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[10] concerns the combinatorial complexity of families of curves in the plane and their applications to motion planning problems[11][12] the maximum number of k-sets and halving lines that a planar point set may have,[13] crossing numbers of graphs,[14][15] embedding of planar graphs onto fixed sets of points,[16][17] and lower bounds for epsilon-nets.[18][19]

Awards and honors

Pach received the Grünwald Medal of the János Bolyai Mathematical Society (1982), the Ford Award from the Mathematical Association of America (1990), and the Alfréd Rényi Prize from the Hungarian Academy of Sciences (1992).[20][21] 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.[22] In 2014 he was elected as a member of Academia Europaea,[23] and in 2015 as a fellow of the American Mathematical Society "for contributions to discrete and combinatorial geometry and to convexity and combinatorics."[24]


  • Pach, János, ed. (1993), New Trends in Discrete and Computational Geometry, Algorithms and Combinatorics, 10, Springer-Verlag, ISBN 978-3-540-55713-5.
  • Pach, János; Agarwal, Pankaj K. (1995), Combinatorial Geometry, Wiley-Interscience Series in Discrete Mathematics and Optimization, John Wiley & Sons, ISBN 978-0-471-58890-0.
  • Aronov, Boris; Basu, Saugata; Pach, János; et al., eds. (2003), Discrete and Computational Geometry: The Goodman–Pollack Festschrift, Algorithms and Combinatorics, 25, Springer-Verlag, ISBN 978-3-540-00371-7.
  • Pach, János, ed. (2004), Towards a Theory of Geometric Graphs, Contemporary Mathematics, 342, American Mathematical Society, ISBN 978-0-8218-3484-8.
  • Pach, János, ed. (2004), Graph Drawing: 12th International Symposium, GD 2004, New York, NY, USA, September 29-October 2, 2004, Lecture Notes in Computer Science, 3383, Springer-Verlag, ISBN 978-3-540-24528-5.
  • Brass, Peter; Moser, W. O. J.; Pach, János, eds. (2005), Research Problems in Discrete Geometry, Springer-Verlag, ISBN 978-0-387-23815-9.
  • Goodman, Jacob E.; Pach, János; Emo, Welzl, eds. (2005), Combinatorial and Computational Geometry, MSRI Publications, 52, Cambridge University Press, ISBN 978-0-521-84862-6.
  • Goodman, Jacob E.; Pach, János; Pollack, Richard, eds. (2008), Surveys on Discrete and Computational Geometry: Twenty Years Later, Contemporary Mathematics, 453, American Mathematical Society, ISBN 978-0-8218-4239-3.
  • Pach, János; Sharir, Micha (2009), Combinatorial Geometry and Its Algorithmic Applications: The Alcalá Lectures, Mathematical Surveys and Monographs, American Mathematical Society, ISBN 978-0-8218-4691-9.
  • Pach, János, ed. (2013), Thirty essays on geometric graph theory, Springer, ISBN 978-1-4614-0110-0.

See also


  1. Bio: Janos Pach, Chair of Combinatorial Geometry École Polytechnique Fédérale de Lausanne (EPFL), Switzerland
  2. János Pach appointed as a full professor of mathematics, EPFL, December 12, 2007.
  3. János Pach at the Mathematics Genealogy Project
  4. Research Fellows, Renyi Institute
  5. Faculty profile, NYU, retrieved 2011-08-15.
  6. List of Speakers at ICM.
  7. Computing Your Erdös Number
  8. Pach, János (1981), "A problem of Ulam on planar graphs", European J. Combin., 2: 357–361, doi:10.1016/s0195-6698(81)80043-1
  9. AMS Meeting
  10. Google scholar, retrieved October 23, 2008.
  11. Kedem, Klara; Livne, Ron; Pach, János; Sharir, Micha (1986), "On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles", Discrete and Computational Geometry, 1 (1): 59–71, doi:10.1007/BF02187683.
  12. Edelsbrunner, Herbert; Guibas, Leonidas J.; Pach, János; Pollack, Richard; Seidel, Raimund; Sharir, Micha, "Arrangements of curves in the plane: topology, combinatorics, and algorithms", 15th Int. Colloq. Automata, Languages and Programming, Lecture Notes in Computer Science, 317, Springer-Verlag, pp. 214–229.
  13. Pach, János; Steiger, William; Szemerédi, Endre (1992), "An upper bound on the number of planar K-sets", Discrete and Computational Geometry, 7 (1): 109–123, doi:10.1007/BF02187829.
  14. Pach, János; Tóth, Géza (1997), "Graphs drawn with few crossings per edge", Combinatorica, 17 (3): 427–439, doi:10.1007/BF01215922.
  15. Pach, János; Tóth, Géza (2000), "Which crossing number is it, anyway?", Journal of Combinatorial Theory, Series B, 80 (2): 225–246, doi:10.1006/jctb.2000.1978.
  16. de Fraysseix, Hubert; Pach, János; Pollack, Richard (1988), "Small sets supporting Fáry embeddings of planar graphs", Proc. 20th ACM Symp. Theory of Computing, pp. 426–433, doi:10.1145/62212.62254.
  17. Pach, János; Wenger, Rephael (2001), "Embedding planar graphs at fixed vertex locations", Graphs and Combinatorics, 17 (4): 717–728, doi:10.1007/PL00007258.
  18. Komlós, János; Pach, János; Woeginger, Gerhard (1992), "Almost tight bounds for ε-nets.", Discrete & Computational Geometry, 7 (2): 163–173, doi:10.1007/bf02187833.
  19. Pach, János; Tardos, Gábor (2013), "Tight lower bounds for the size of epsilon-nets", J. Amer. Math. Soc., 26: 645–658, arXiv:1012.1240, doi:10.1090/s0894-0347-2012-00759-0.
  20. "Rényi-díj". Alfred Rényi Institute of Mathematics. Retrieved 8 March 2010.
  21. Short biography, from SFU Computing Science.
  22. ACM Names Fellows for Computing Advances that Are Driving Innovation, Association for Computing Machinery, December 8, 2011.
  23. Academia Europaea-List of Members, retrieved 2018-04-06.
  24. 2016 Class of the Fellows of the AMS, American Mathematical Society, retrieved 2015-11-16.
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