Jonathan Pila

Jonathan Pila (2015)

Jonathan S. Pila (born around 1960) is an Australian mathematician .

Life

Jonathan Pila studied mathematics and received a Bachelor of Science with Honors in Melbourne in 1984 . In 1988 he was at Stanford University with a thesis on Frobenius Maps of Abelian Varieties and Finding Roots of Unity in Finite Fields for Ph.D. PhD . His doctoral supervisor was Peter Sarnak . Pila is a reader at the University of Oxford .

Pila deals with model theory and number theory . With Umberto Zannier he developed a method to apply the theory of O-minimality to number theoretic and algebro-geometric problems and they gave a renewed proof of the Manin-Mumford conjecture (originally by Michel Raynaud and proven within the model theory of Ehud Hrushovski ). He proved the André-Oort conjecture (named after Yves André and Frans Oort ) for products of modular curves and for the first time without assuming the generalized Riemann conjecture and with the help of O-minimality. He continued his work on the André Oort conjecture from 2009 in collaboration with Jacob Tsimerman . For this he received the Clay Research Award and the Senior Whitehead Prize in 2011 . In 2013 he gave the Tarski Lectures . He was selected as plenary speaker at the International Congress of Mathematicians 2014 in Seoul (O-minimality and Diophantine geometry). In 2015 Pila was elected to the Royal Society and in 2016 to the Academia Europaea .

O-minimality and the André-Oort conjecture for . ${\ displaystyle \ mathbb {C} ^ {n}}$ In: Annals of Mathematics. Volume 173, 2011, pp. 1779-1840
with Alex Wilkie : The rational points of a definable set. In: Duke Mathematical Journal. Volume 133, 2006, pp. 591-616
with U. Zannier: Rational points in periodic analytic sets and the Manin-Mumford conjecture. In: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni. Series 9, Volume 19, 2008, No. 2, pp. 149-162.

Thomas Scanlon: A proof of the André-Oort-Conjecture via Mathematical Logic. After Pila, Wilkie, Zannier . Seminaire Bourbaki, No. 1037, April 2011, pdf

Jonathan S. Pila in the Mathematics Genealogy Project (English)
Dr Jonathan Pila on the University of Oxford Mathematical Institute website
Dr Jonathan Pila on the University of Bristol's School of Mathematics website
Jonathan Pila - Diophantine Geometry via O-Minimality Video of a lecture by Pila at the Clay Research Conference 2011

^ O-minimality and the André-Oort conjecture for . ${\ displaystyle \ mathbb {C} ^ {n}}$ In: Annals of Mathematics. Volume 173, 2011, pp. 1779–1840, doi: 10.4007 / annals.2011.173.3.11 , preprint (PDF; 338 kB)
↑ on the website of the Clay Mathematics Institute; Jonathan Pila receives a 2011 Clay Research Award ( Memento of the original from May 30, 2011 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice. on the website of the Mathematical Institute of the University of Oxford @1@ 2

↑ Citations for LMS prize winners on the London Mathematical Society website, April 28, 2011