János Pach

János Pach
Name	János Pach
Birth date	1954
Birth place	Budapest, Hungary
Nationality	Hungarian
Fields	Mathematics, Computer Science
Workplaces	Rényi Institute, École Polytechnique, University of Minnesota, TU Berlin
Alma mater	Eötvös Loránd University
Known for	Combinatorial geometry, Graph drawing, Combinatorics, Discrete geometry

János Pach is a Hungarian mathematician and computer scientist noted for foundational work in combinatorial geometry, graph drawing, and discrete geometry. His career spans research institutes and universities across Europe and North America, and his publications and collaborations have influenced topics connected to Paul Erdős, László Lovász, and the wider community surrounding the Rényi Institute. He has authored influential monographs and numerous papers that connect classical problems with algorithmic and combinatorial methods.

Early life and education

Pach was born in Budapest and completed his early studies at institutions in Hungary, including Eötvös Loránd University. During his formative years he came under the influence of the Hungarian mathematical culture associated with figures like Paul Erdős and Paul Turán, and was exposed to problem-solving traditions linked to the Mathematical Olympiad movement. His doctoral work and early publications engaged with problems that later connected to themes explored by Pál Erdős collaborators and researchers at the Alfréd Rényi Institute of Mathematics.

Academic career and positions

Pach held research and faculty positions at several prominent institutions. He worked at the Alfréd Rényi Institute of Mathematics (often called the Rényi Institute), and took appointments at universities including the University of Minnesota, École Polytechnique, and Technische Universität Berlin. He also collaborated with researchers at institutes such as the Institute for Advanced Study, the Massachusetts Institute of Technology, and the Bell Labs research community during visits and joint projects. Throughout his career he maintained ties with the Hungarian academic system and international networks including the International Mathematical Union and conferences organized by groups like the Society for Industrial and Applied Mathematics.

Research contributions and selected works

Pach’s research addresses a spectrum of problems in combinatorial geometry and graph theory, often connecting extremal questions with geometric constructions and algorithmic implications. He co-authored influential books and survey articles that synthesized developments in discrete geometry and popularized approaches to problems studied by researchers such as Branko Grünbaum, Erdős–Szekeres, and Paul Erdős. Notable contributions include work on the crossing number of graphs, incidences between points and lines, and the combinatorics of geometric graphs, related to problems investigated by Miklós Simonovits, László Lovász, and Bálint Tóth.

Selected works include monographs and edited volumes that discuss topics aligned with the research agendas of Jacob Fox, Terence Tao, and József Solymosi; papers that established bounds and structural results referencing methods from Szemerédi regularity lemma frameworks and techniques connected to Elekes–Rónyai style incidence problems; and collaborations on algorithmic aspects related to planarity testing, graph drawing conventions, and combinatorial bounds reminiscent of problems tackled by Noga Alon and Joel Spencer. His joint work with collaborators produced results on geometric hypergraphs, Tverberg-type theorems connected to Helge Tverberg, and Ramsey-type phenomena in geometric contexts related to Frankl–Wilson style combinatorics.

Awards and honors

Pach’s contributions have been recognized by invitations to prominent conferences and editorial roles for journals linked to the communities around Combinatorica, Discrete & Computational Geometry, and other professional venues. He has received honors and distinctions from Hungarian institutions such as the Hungarian Academy of Sciences and international recognition through invited lectures at gatherings including the International Congress of Mathematicians satellite events and workshops organized by the American Mathematical Society and the European Mathematical Society. His influence is evident in citations and in the adoption of his results in work by scholars like Jacob Fox, Nikolai Alon, and Endre Szemerédi.

Teaching and mentoring

Throughout his tenure at institutions such as the University of Minnesota and École Polytechnique, Pach supervised graduate students and postdoctoral researchers who went on to positions in academia and industry, contributing to networks associated with Combinatorics research groups and centers. He gave advanced courses and seminars on topics tied to the legacies of Paul Erdős and Gábor Szekeres, and served on doctoral committees alongside members of the Rényi Institute and faculty from departments including those at TU Berlin and Eötvös Loránd University. His mentorship fostered collaborations that bridged combinatorics, computational geometry, and algorithmic graph theory, influencing researchers such as József Solymosi and others active in geometric combinatorics.

Personal life and interests

Outside academic work, Pach has engaged with the Hungarian mathematical community and outreach venues associated with the Mathematical Olympiad tradition and public lectures at institutions like the House of Hungarian Science events. His interests reflect the broader cultural and intellectual milieu tied to Budapest's scientific scene and the European networks of mathematics, including participation in symposia alongside figures from the Institute for Advanced Study and connections to research programs at institutions such as CNRS and Max Planck Institute.

Category:Hungarian mathematicians Category:Graph theorists Category:Combinatorial geometers