Roger Heath-Brown
{{Short description|British mathematician}}
{{EngvarB|date=July 2017}}
{{Use dmy dates|date=July 2017}}
{{Infobox scientist
| name = Roger Heath-Brown
| honorific_suffix = {{postnominals|country=GBR|size=100%|OBE|FRS}}
| image = Roger Heath-Brown.jpg
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| caption = Heath-Brown in 1986
| birth_date = {{Birth date and age|df=yes|1952|10|12}}
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| citizenship = United Kingdom
| fields = Pure mathematics
| workplaces = University of Oxford
| alma_mater = University of Cambridge
| doctoral_advisor = Alan Baker
| academic_advisors =
| doctoral_students = Timothy Browning
Timothy Trudgian
James Maynard
| notable_students =
| thesis_title = Topics in Analytic Number Theory
| thesis_year = 1979
| known_for = Analytic number theory, Heath-Brown–Moroz constant
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| awards = Smith's Prize (1976)
Berwick Prize (1981)
Fellow of the Royal Society (1993)
Senior Berwick Prize (1996)
Pólya Prize (2009)
Sylvester Medal (2022)
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| website = {{URL|www.maths.ox.ac.uk/people/roger.heath-brown}}
}}
David Rodney "Roger" Heath-Brown is a British mathematician working in the field of analytic number theory.{{cite web
|title=Prof. Roger Heath-Brown, University of Oxford, FRS
|url=https://www.maths.ox.ac.uk/people/roger.heath-brown
|access-date=4 May 2017
}}
Education
He was an undergraduate and graduate student of Trinity College, Cambridge; his research supervisor was Alan Baker.[http://www.maths.ox.ac.uk/perl/personal-details.pl?query=rhb Official home page] {{webarchive|url=https://web.archive.org/web/20040805134939/http://www.maths.ox.ac.uk/perl/personal-details.pl?query=rhb |date=5 August 2004 }}{{MathGenealogy |id=70392}}
Career and research
In 1979 he moved to the University of Oxford, where from 1999 he held a professorship in pure mathematics.{{cite web|title=Prof Roger Heath-Brown, FRS|url=http://www.debretts.com/people/biographies/browse/h/18035/David%20Rodney%20%28Roger%29+HEATH-BROWN.aspx|work=Debrett's People of Today|access-date=28 December 2010|url-status=dead|archive-url=https://web.archive.org/web/20120906034250/http://www.debretts.com/people/biographies/browse/h/18035/David%20Rodney%20%28Roger%29+HEATH-BROWN.aspx|archive-date=6 September 2012|df=dmy-all}} He retired in 2016.[https://gazette.web.ox.ac.uk/sites/default/files/gazette/documents/media/vice-chancellors_oration_2016_-_1_to_no_5144.pdf "Vice chancellor's oration"]. Gazette.web.ox.ac.uk. Retrieved on 2018-08-29.
Heath-Brown is known for many striking results. He proved that there are infinitely many prime numbers of the form x3 + 2y3.{{Cite journal | last1 = Heath-Brown |first1 = D.R.| title = Primes represented by x3 + 2y3| journal = Acta Mathematica | volume = 186 | pages = 1–84| year = 2001 | doi = 10.1007/BF02392715| doi-access = free}}
In collaboration with S. J. Patterson in 1978 he proved the Kummer conjecture on cubic Gauss sums in its equidistribution form.
He has applied Burgess's method on character sums to the ranks of elliptic curves in families.
He proved that every non-singular cubic form over the rational numbers in at least ten variables represents 0.{{cite journal | doi=10.1112/plms/s3-47.2.225 | title=Cubic Forms in Ten Variables | year=1983 | last1=Heath-Brown | first1=D. R. | journal=Proceedings of the London Mathematical Society |series=Series 3 |volume=47 | issue=2 | pages=225–257 }}
Heath-Brown also showed that Linnik's constant is less than or equal to 5.5.{{cite journal | doi=10.1112/plms/s3-64.2.265 | title=Zero-Free Regions for Dirichlet L-Functions, and the Least Prime in an Arithmetic Progression | year=1992 | last1=Heath-Brown | first1=D. R. | journal=Proceedings of the London Mathematical Society |series=Series 3 |volume=64 | issue=2 | pages=265–338 | url=https://ora.ox.ac.uk/objects/uuid:b63b8b4f-ad21-4de4-a86b-c82fdfc87997 }} More recently, Heath-Brown is known for his pioneering work on the so-called determinant method. Using this method he was able to prove a conjecture of Serre{{cite journal | last1=Castryck | first1=Wouter | last2=Cluckers | first2=Raf | last3=Dittmann | first3=Philip | last4=Nguyen | first4=Kien Huu | title=The dimension growth conjecture, polynomial in the degree and without logarithmic factors | journal=Algebra & Number Theory | year=2020 | volume=14 | issue=8 | pages=2261–2294 | doi=10.2140/ant.2020.14.2261 |arxiv=1904.13109| s2cid=140223593 }} in the four variable case in 2002.{{cite journal | jstor=3062125 | last1=Heath-Brown | first1=D. R. | title=The Density of Rational Points on Curves and Surfaces | journal=Annals of Mathematics | year=2002 | volume=155 | issue=2 | pages=553–598 | doi=10.2307/3062125 | arxiv=math/0405392 | s2cid=15167809 }} This particular conjecture of Serre was later dubbed the "dimension growth conjecture" and this was almost completely solved by various works of Browning, Heath-Brown, and Salberger by 2009.{{cite book | doi=10.1007/978-3-0346-0129-0 | title=Quantitative Arithmetic of Projective Varieties | year=2009 | last1=Browning | first1=Timothy D. | isbn=978-3-0346-0128-3 }}
Honours and awards
The London Mathematical Society has awarded Heath-Brown the Junior Berwick Prize (1981), the Senior Berwick Prize (1996),[http://www-groups.dcs.st-and.ac.uk/~history/Societies/LMSBerwick.html Berwick prizes page at The MacTutor History of Mathematics archive] and the Pólya Prize (2009). He was made a Fellow of the Royal Society in 1993, and a corresponding member of the Göttingen Academy of Sciences in 1999.{{cite web|title=Professor Roger Heath-Brown|url=http://www.maths.ox.ac.uk/contact/details/rhb|publisher=The Mathematical Institute, University of Oxford|access-date=28 December 2010}}
He was an invited speaker at International Congress of Mathematicians in 1983 in Warsaw and in 2010 in Hyderabad on the topic of "Number Theory."{{cite web|title=ICM Plenary and Invited Speakers since 1897|url=https://www.mathunion.org/icm-plenary-and-invited-speakers?combine=heath|publisher=International Congress of Mathematicians}}
In 2012 he became a fellow of the American Mathematical Society.[https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society]. Retrieved 19 January 2013. In 2022 the Royal Society awarded him the Sylvester Medal "for his many important contributions to the study of prime numbers and solutions to equations in integers".{{cite web |title=Roger Heath-Brown awarded the Sylvester Medal|publisher=The Mathematical Institute, University of Oxford |url=https://www.maths.ox.ac.uk/node/61066 |website=www.maths.ox.ac.uk|access-date=2023-01-05|date=24 August 2022}}
Heath-Brown was appointed Officer of the Order of the British Empire (OBE) in the 2024 New Year Honours for services to mathematics and mathematical research.{{London Gazette|issue=64269|supp=y|page=N12|date=30 December 2023}}
Other
In September 2007, he co-authored (along with Joseph H. Silverman) the preface to the Oxford University Sixth Edition of the classic text An Introduction to the Theory of Numbers by G.H. Hardy and E.M. Wright.
References
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Category:Alumni of Trinity College, Cambridge
Category:20th-century British mathematicians
Category:21st-century British mathematicians
Category:Fellows of Magdalen College, Oxford
Category:Fellows of Worcester College, Oxford
Category:Fellows of the Royal Society
Category:Fellows of the American Mathematical Society