József Solymosi

Jozsef, Solymosi, Oberwolfach 2017

József Solymosi (born November 10, 1959 ) is a Hungarian-Canadian mathematician who deals with combinatorics .

Life

Solymosi received his master's degree from the Lorand Eötvös University in Budapest (with László Székely ) in 1999 and received his doctorate in 2001 with Emo Welzl at the ETH Zurich ( Ramsey-type results on planar geometric objects ). From 2001 to 2003 he was SE Warschawski Assistant Professor at the University of California, San Diego and from 2002 Assistant Professor at the University of British Columbia , where he became Associate Professor in 2007 and Professor in 2011.

In 2007/08 he was at the Institute for Advanced Study . In 2010 he was visiting professor at EPFL in Lausanne, in 2014 at the University of California, Los Angeles , and in 2019 at Yale University . In 2018/19 he conducted research at the Alfred Renyi Institute in Budapest and in 2011 he was a visiting scholar at the Isaac Newton Institute .

Solymosi showed in 2003 that if in a finite set of points on the Euclidean plane every pair of points has an integer distance, the diameter of the set must be linear in the number of points. This is related to the theorem of Erdös and Anning , according to which an infinite number of points of the Euclidean plane with an integer distance between the points must lie on a straight line.

In the context of the (open) Erdös-Ulam problem (which asks whether there is a dense subset of the plane whose points all have rational distances from one another) he proved with Frank de Zeeuw that the only irreducible algebraic curves are the infinite number of points with rational distances from one another, the circle and the straight line are.

With Terence Tao he generalized the theorem of Szemerédi and Trotter , according to which the number of incidences of n points and m lines in the Euclidean plane is of the order of magnitude . Tao and Solymosi considered arbitrary Euclidean spaces of finite dimension and incidences between n points and m affine subspaces, where each pair of subspaces has at most one point of intersection. They showed for the number of incidences ${\ displaystyle O ({(nm)} ^ {\ frac {2} {3}} + n + m)}$ ${\ displaystyle O ({(nm)} ^ {{\ frac {2} {3}} + \ varepsilon}}$

He improved the barriers in the problem of different distances from Erdős in the plane as well as in higher dimensions.

He made improvements to the sentence by Erdös and Szemerédi. This means that for a finite set of real numbers A there is a constant c , such that ${\ displaystyle \ epsilon}$

{\ displaystyle \ max (| A + A |, | A \ cdot A |) \ geq c | A | ^ {1+ \ varepsilon}}

Solymosi showed that anywhere near a third is. ${\ displaystyle \ epsilon}$

He was wearing for the first Polymath project by Timothy Gowers at, which is to make improvements to the set of Hales and Jewett went.

In 2006 he became a Sloan Research Fellow and in 2008 he received the André Aisenstadt Prize . In 2012 he received an honorary doctorate from the Hungarian Academy of Sciences. From 2013 to 2015 he was editor of the Electronic Journal of Combinatorics.

Fonts

with C. Tóth: Distinct distances in the plane , Discrete & Computational Geometry, Volume 25, 2001, pp .: 629–634
with Noga Alon , J. Pach: Ramsey-type theorems with forbidden subgraphs , Combinatorica, Volume 21, 2001, pp. 155-170
Note on integral distances , Discrete & Computational Geometry, Volume 30, 2003, pp. 337-342
On the number of sums and products , Bulletin of the London Mathematical Society, Volume 37, 2005, pp. 491-494
with Van H. Vu : Near optimal bounds for the Erdős distinct distances problem in high dimensions , Combinatorica, Volume 28, 2008, pp. 113–125
Bounding multiplicative energy by the sumset , Advances in Mathematics, Volume 222, 2009, pp. 402-408
with Frank de Zeeuw: On a question of Erdős and Ulam , Discrete & Computational Geometry, Volume 43, 2010, pp. 393–401
with Terence Tao: An incidence theorem in higher dimensions , Discrete & Computational Geometry, Volume 48, 2012, pp. 255–280

Web links

Homepage
CV

Individual evidence

↑ József Solymosi in the Mathematics Genealogy Project (English)
↑ Michael Nielsen, Reinventing Discovery: The New Era of Networked Science, Princeton University Press, 2012

personal data
SURNAME	Solymosi, József
ALTERNATIVE NAMES	Solymosi, Jozsef
BRIEF DESCRIPTION	Hungarian-Canadian mathematician
DATE OF BIRTH	November 10, 1959

[1] József Solymosi in the Mathematics Genealogy Project (English)

[2] Michael Nielsen, Reinventing Discovery: The New Era of Networked Science, Princeton University Press, 2012