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, mathematical structure, structure, space, Mathematica ...

at the

University of Oxford The University of Oxford is a collegiate university, collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the List of oldest un ...

University of Melbourne The University of Melbourne (colloquially known as Melbourne University) is a public university, public research university located in Melbourne, Australia. Founded in 1853, it is Australia's second oldest university and the oldest in the state ...

in 1984. He was awarded a PhD from

Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...

in 1988, for research supervised by Peter Sarnak. 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

Research interests lie in

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

and

model theory In mathematical logic, model theory is the study of the relationship between theory (mathematical logic), formal theories (a collection of Sentence (mathematical logic), sentences in a formal language expressing statements about a Structure (mat ...

. 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) 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 Mathematics ...

, and developed through collaborations with Alex Wilkie and Umberto Zannier. 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. Pila has held posts at

Columbia University Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Churc ...

McGill University McGill University (French: Université McGill) is an English-language public research university in Montreal, Quebec, Canada. Founded in 1821 by royal charter,Frost, Stanley Brice. ''McGill University, Vol. I. For the Advancement of Learning, ...

, the

University of Bristol The University of Bristol is a public university, public research university in Bristol, England. It received its royal charter in 1909, although it can trace its roots to a Merchant Venturers' school founded in 1595 and University College, Br ...

and (as a visiting member) the

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

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

Awards and honours

Pila was awarded the Clay Research Award 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 by the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's Learned society, learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh ...

. 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 conjectures. The approach he and his collaborators have developed, which combines analytic ideas with

, 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 in 2013. Pila was elected a Fellow of the Royal Society (FRS) in 2015. In 2022, he received the Rolf Schock Prize in the category of "Mathematics".

References

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