Jonathan Solomon Pila (born 1962) FRS One or more of the preceding sentences incorporates text from the royalsociety.org website where: is an Australian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

at the

University of Oxford , mottoeng = The Lord is my light , established = , endowment = £6.1 billion (including colleges) (2019) , budget = £2.145 billion (2019–20) , chancellor ...

Education

Pila earned his bachelor's degree at the

University of Melbourne The University of Melbourne is a public research university located in Melbourne, Australia. Founded in 1853, it is Australia's second oldest university and the oldest in Victoria. Its main campus is located in Parkville, an inner suburb no ...

in 1984. He was awarded a PhD from Stanford University in 1988, for research supervised by

Peter Sarnak Peter Clive Sarnak (born 18 December 1953) is a South African-born mathematician with dual South-African and American nationalities. Sarnak has been a member of the permanent faculty of the School of Mathematics at the Institute for Advanced St ...

. His dissertation was entitled "Frobenius Maps of Abelian Varieties and Finding Roots of Unity in Finite Fields". In 2010 he received an MA from Oxford.

Career and research

Pila's research interests lie in

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mat ...

and model theory. A focus has been applying the theory of o-minimality to Diophantine problems. This work began with an early paper with

Enrico Bombieri Enrico Bombieri (born 26 November 1940, Milan) is an Italian mathematician, known for his work in analytic number theory, Diophantine geometry, complex analysis, and group theory. Bombieri is currently Professor Emeritus in the School of Mathem ...

, and developed through collaborations with

Alex Wilkie Alex James Wilkie FRS (born 1948 in Northampton) is a British mathematician known for his contributions to model theory and logic. Previously Reader in Mathematical Logic at the University of Oxford, he was appointed to the Fielden Chair of Pur ...

and

Umberto Zannier Umberto Zannier (born 25 May 1957, in Spilimbergo, Italy) is an Italian mathematician, specializing in number theory and Diophantine geometry. Education Zannier earned a Laurea degree from University of Pisa and studied at the Scuola Normale Sup ...

. The techniques obtained have led to advances in Diophantine problems, including Pila's unconditional proof of the André–Oort conjecture for powers of the modular curve. Work by Pila and Jacob Tsimerman, demonstrated the André–Oort conjecture in the case of the

Siegel modular variety In mathematics, a Siegel modular variety or Siegel moduli space is an algebraic variety that parametrizes certain types of abelian varieties of a fixed dimension. More precisely, Siegel modular varieties are the moduli spaces of principally pola ...

. Pila has held posts at

Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...

McGill University McGill University (french: link=no, Université McGill) is an English-language public research university located in Montreal, Quebec Montreal ( ; officially Montréal, ) is the second-most populous city in Canada and most populous ...

, the

University of Bristol , mottoeng = earningpromotes one's innate power (from Horace, ''Ode 4.4'') , established = 1595 – Merchant Venturers School1876 – University College, Bristol1909 – received royal charter , type ...

and (as a visiting member) the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent schola ...

. Pila also took a substantial break from professional mathematics to work in his family's manufacturing business. Pila has been the Editor of Proceedings of the ''

Edinburgh Mathematical Society The Edinburgh Mathematical Society is a mathematical society for academics in Scotland. History The Society was founded in 1883 by a group of Edinburgh school teachers and academics, on the initiative of Alexander Yule Fraser FRSE and Andrew Je ...

'', and of '' Algebra and Number Theory''.

Awards and honours

Pila was awarded the

Clay Research Award __NOTOC__ The Clay Research Award is an annual award given by the Oxford-based Clay Mathematics Institute to mathematicians to recognize their achievement in mathematical research. The following mathematicians have received the award: {, class=" ...

in 2011 for his resolution of the André–Oort conjecture in the case of products of modular curves. In June 2011, he was awarded the

Senior Whitehead Prize The Senior Whitehead Prize of the London Mathematical Society (LMS) is now awarded in odd numbered years in memory of John Henry Constantine Whitehead, president of the LMS between 1953 and 1955. The Prize is awarded to mathematicians normally ...

by the London Mathematical Society. This prize is "awarded in recognition of work in and influence on and service to mathematics; or lecturing gifts." Specifically, the citation recognized "his startling recent work on the Andre-Oort and

Manin-Mumford conjecture In mathematics, the arithmetic of abelian varieties is the study of the number theory of an abelian variety, or a family of abelian varieties. It goes back to the studies of Pierre de Fermat on what are now recognized as elliptic curves; and has ...

s. The approach he and his collaborators have developed, which combines analytic ideas with model theory, is entirely new and shows great promise for further applications." In addition to the Clay and London Mathematical Society awards, Pila delivered the Arf Lecture in 2011, was awarded the Leverhulme Trust Research Fellowship 2008–2010. and received the

Karp Prize The Association for Symbolic Logic (ASL) is an international organization of specialists in mathematical logic and philosophical logic. The ASL was founded in 1936, and its first president was Alonzo Church. The current president of the ASL i ...

in 2013. Pila was elected a Fellow of the Royal Society (FRS) in 2015. In 2022 he received the

Rolf Schock Prize The Rolf Schock Prizes were established and endowed by bequest of philosopher and artist Rolf Schock (1933–1986). The prizes were first awarded in Stockholm, Sweden, in 1993 and, since 2005, are awarded every three years. Each recipient current ...

in the category of "Mathematics".Rolf Schock Prize 2022
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References

{{DEFAULTSORT:Pila, Jonathan 1962 births Living people Australian mathematicians University of Melbourne alumni Stanford University alumni Number theorists Clay Research Award recipients Tarski lecturers Australian Fellows of the Royal Society Academics of the University of Oxford