View source for József Solymosi

{{short description|Hungarian-Canadian mathematician}}
{{Infobox scientist
| name              = 
| image             = József Solymosi Oberwolfach 2024.jpg
| landscape         = yes
| caption           = Solymosi in [[Oberwolfach Research Institute for Mathematics|Oberwolfach]], 2024
| nationality       = 
| fields            = [[Mathematics]]
| workplaces        = [[University of British Columbia]]
| alma_mater        = [[ETH Zürich]]
| thesis_title      = Ramsey-Type Results on Planar Geometric Objects
| thesis_year       = 2001
| doctoral_advisor  = [[Emo Welzl]]
| doctoral_students = 
| known_for         = 
| awards            = 
}}
{{distinguish|text = swimmer [[Jozef Solymosy]]}}

'''József Solymosi''' is a Hungarian-Canadian mathematician and a professor of mathematics at the [[University of British Columbia]]. His main research interests are [[arithmetic combinatorics]], [[discrete geometry]], [[graph theory]], and [[combinatorial number theory]].{{r|cv}}

==Education and career==
Solymosi earned his master's degree in 1999 under the supervision of László Székely from the [[Eötvös Loránd University]]{{r|szekstud}} and his Ph.D. in 2001 at [[ETH Zurich|ETH Zürich]] under the supervision of [[Emo Welzl]]. His doctoral dissertation was ''Ramsey-Type Results on Planar Geometric Objects''.{{r|mgp}}

From 2001 to 2003 he was [[Stefan E. Warschawski|S. E. Warschawski]] Assistant Professor of Mathematics at the [[University of California, San Diego]]. He joined the faculty of the University of British Columbia in 2002.{{r|cv}}

He was [[editor in chief]] of the ''[[Electronic Journal of Combinatorics]]''{{r|ejc}} from 2013 to 2015.

==Contributions==
Solymosi was the first online contributor to the first [[Polymath Project]], set by [[Timothy Gowers]] to find improvements to the [[Hales–Jewett theorem]].{{r|nielsen}}

One of his theorems states that if a finite set of points in the [[Euclidean plane]] has every pair of points at an integer distance from each other, then
the set must have a [[diameter]] (largest distance) that is linear in the number of points. This result is connected to the [[Erdős–Anning theorem]], according to which an infinite set of points with integer distances must lie on one line.{{r|gis}}{{ran|ID}} In connection with the related [[Erdős–Ulam problem]], on the existence of dense subsets of the plane for which all distances are rational numbers, Solymosi and de Zeeuw proved that every infinite rational-distance set must either be dense in the [[Zariski topology]] or it must have all but finitely many of its points on a single line or circle.{{r|erdosulam}}{{ran|EU}}

With [[Terence Tao]], Solymosi proved a bound of <math>(mn)^{2/3+\varepsilon}</math> on the number of incidences between <math>n</math> points and <math>m</math> affine subspaces of any finite-dimensional Euclidean space, whenever each pair of subspaces has at most one point of intersection. This generalizes the [[Szemerédi–Trotter theorem]] on points and lines in the Euclidean plane, and because of this the exponent of <math>2/3</math> cannot be improved. Their theorem solves (up to the <math>\varepsilon</math> in the exponent) a conjecture of Toth, and was inspired by an analogue of the Szemerédi–Trotter theorem for lines in the [[complex plane]].{{r|guth|ithd}}{{ran|HD}}

He has also contributed improved bounds for the [[Erdős–Szemerédi theorem]], showing that every set of real numbers has either a large set of pairwise sums or a large set of pairwise products,{{r|sumprod}}{{ran|ME}} and for the [[Erdős distinct distances problem]], showing that every set of points in the plane has many different pairwise distances.{{r|distdist}}{{ran|DD}}

==Recognition==
In 2006, Solymosi received a [[Sloan Research Fellowship]]{{r|sloan}} and in 2008 he was awarded the [[Aisenstadt Prize|André Aisenstadt Mathematics Prize]].{{r|aisenstadt}} In 2012 he was named a doctor of the [[Hungarian Academy of Science]].{{r|mtadoc}}

==Selected publications==
{{rma|DD|tw=2em|{{citation
 | last1 = Solymosi | first1 = J.
 | last2 = Tóth | first2 = Cs. D.
 | doi = 10.1007/s00454-001-0009-z
 | issue = 4
 | journal = [[Discrete & Computational Geometry]]
 | mr = 1838423
 | pages = 629–634
 | title = Distinct distances in the plane
 | volume = 25
 | year = 2001| doi-access = free
 }}}}

{{rma|ID|tw=2em|{{citation
 | last = Solymosi | first = József
 | doi = 10.1007/s00454-003-0014-7
 | issue = 2
 | journal = [[Discrete & Computational Geometry]]
 | mr = 2007970
 | pages = 337–342
 | title = Note on integral distances
 | volume = 30
 | year = 2003| doi-access = free
 }}}}

{{rma|ME|tw=2em|{{citation
 | last = Solymosi | first = József
 | doi = 10.1016/j.aim.2009.04.006 | doi-access=free
 | issue = 2
 | journal = [[Advances in Mathematics]]
 | mr = 2538014
 | pages = 402–408
 | title = Bounding multiplicative energy by the sumset
 | volume = 222
 | year = 2009| arxiv = 0806.1040
 }}}}

{{rma|EU|tw=2em|{{citation
 | last1 = Solymosi | first1 = Jozsef
 | last2 = de Zeeuw | first2 = Frank
 | doi = 10.1007/s00454-009-9179-x
 | issue = 2
 | journal = [[Discrete & Computational Geometry]]
 | mr = 2579704
 | pages = 393–401
 | title = On a question of Erdős and Ulam
 | volume = 43
 | year = 2010| doi-access = free
 | arxiv = 0806.3095
 }}}}

{{rma|HD|tw=2em|{{citation
 | last1 = Solymosi | first1 = József
 | last2 = Tao | first2 = Terence | author2-link = Terence Tao
 | doi = 10.1007/s00454-012-9420-x
 | issue = 2
 | journal = [[Discrete & Computational Geometry]]
 | mr = 2946447
 | pages = 255–280
 | title = An incidence theorem in higher dimensions
 | volume = 48
 | year = 2012| arxiv = 1103.2926
 | s2cid = 17830766
 }}}}

==References==
{{reflist|refs=

<ref name=aisenstadt>{{citation|url=https://www.ams.org/notices/200802/tx080200264p.pdf|journal=[[Notices of the American Mathematical Society]]|department=Mathematics People|title=Solymosi and Taylor Awarded Aisenstadt Prize|page=266|volume=55|issue=2|date=February 2008}}</ref>

<ref name=cv>{{citation|url=http://www.math.ubc.ca/~solymosi/CVshort.html|title=Short curriculum vitae|accessdate=2018-09-08}}</ref>

<ref name=distdist>{{harvtxt|Guth|2016|page=83}}</ref>

<ref name=ejc>{{citation|url=http://www.combinatorics.org/ojs/index.php/eljc/about/editorialTeam|title=Editorial team|journal=[[Electronic Journal of Combinatorics]]|accessdate=2018-09-08}}</ref>

<ref name=erdosulam>{{citation|url=https://terrytao.wordpress.com/2014/12/20/the-erdos-ulam-problem-varieties-of-general-type-and-the-bombieri-lang-conjecture/|first=Terence|last=Tao|authorlink=Terence Tao|date=December 20, 2014|work=What's New|title=The Erdős–Ulam problem, varieties of general type, and the Bombieri–Lang conjecture}}</ref>

<ref name=gis>{{citation
 | last1 = Garibaldi | first1 = Julia
 | last2 = Iosevich | first2 = Alex
 | last3 = Senger | first3 = Steven
 | isbn = 978-0-8218-5281-1
 | mr = 2721878
 | page = [https://books.google.com/books?id=SzCIAwAAQBAJ&pg=PA16 16]
 | publisher = American Mathematical Society, Providence, RI
 | series = Student Mathematical Library
 | title = The Erdős Distance Problem
 | title-link = The Erdős Distance Problem
 | volume = 56
 | year = 2011}}</ref>

<ref name=guth>{{citation
 | last = Guth | first = Larry
 | isbn = 978-1-4704-2890-7
 | mr = 3495952
 | pages = 89–90
 | publisher = American Mathematical Society, Providence, RI
 | series = University Lecture Series
 | title = Polynomial Methods in Combinatorics
 | url = https://books.google.com/books?id=t9ZTDAAAQBAJ&pg=PA89
 | volume = 64
 | year = 2016}}</ref>

<ref name=ithd>{{citation|url=https://terrytao.wordpress.com/2011/03/17/an-incidence-theorem-in-higher-dimensions/|first=Terence|last=Tao|authorlink=Terence Tao|date=March 17, 2011|work=What's New|title=An incidence theorem in higher dimensions|arxiv=1103.2926 }}</ref>

<ref name=mgp>{{mathgenealogy|id=54429}}</ref>

<ref name=mtadoc>{{citation|url=http://mta.hu/koztestuleti_tagok?PersonId=22844|title=Solymosi József|work=Az MTA köztestületének tagjai [Members of the public body of MTA]|language=Hungarian|accessdate=2018-09-08}}</ref>

<ref name=nielsen>{{citation|title=Reinventing Discovery: The New Era of Networked Science|first=Michael|last=Nielsen|publisher=Princeton University Press|year=2012|isbn=9780691148908|page=1|url=https://books.google.com/books?id=afqfFW8WV9cC&pg=PA1}}</ref>

<ref name=sloan>{{citation|url=https://sloan.org/storage/app/media/files/annual_reports/2006_annual_report.pdf|year=2006|title=Annual Report|publisher=Alfred P. Sloan Foundation|accessdate=2018-09-08}}</ref>

<ref name=sumprod>{{citation|url=https://terrytao.wordpress.com/2008/06/17/the-sum-product-phenomenon-in-arbitrary-rings/|first=Terence|last=Tao|authorlink=Terence Tao|date=June 17, 2008|work=What's New|title=The sum-product phenomenon in arbitrary rings|arxiv=0806.2497 }}</ref>

<ref name=szekstud>{{citation|url=http://people.math.sc.edu/laszlo/students.html|title=László Székely's Students|publisher=University of South Carolina|accessdate=2018-09-08}}</ref>

}}

==External links==
*[http://www.math.ubc.ca/~solymosi/ Home page]
*{{Google Scholar id|-t18JkQAAAAJ}}

{{authority control}}

{{DEFAULTSORT:Solymosi, Jozsef}}
[[Category:Year of birth missing (living people)]]
[[Category:Living people]]
[[Category:Canadian mathematicians]]
[[Category:20th-century Hungarian mathematicians]]
[[Category:21st-century Hungarian mathematicians]]
[[Category:Eötvös Loránd University alumni]]
[[Category:ETH Zurich alumni]]
[[Category:Academic staff of the University of British Columbia]]
[[Category:Combinatorialists]]
[[Category:Graph theorists]]