Education

BSc (Hons) Mathematics

University of Melbourne (1984)

PhD Mathematics

Stanford University (1988)

Publications

The number of integral points on arcs and ovals (1989)
Enrico Bombieri, Jonathan Pila
Duke Math. J. vol: 59 , Pages: 337 - 357

The rational points of a definable set (2006)
Jonathan Pila, A. J. Wilkie
Duke Math. J. vol: 133 , Pages: 591 - 616

Full list of publications

Research Interests

Number theory, especially algorithmic and diophantine problems.

My work in algorithmic number theory focuses on the computational complexity of counting rational points on varieties defined over finite fields; that is, of computing the congruence zeta functions of algebraic varieties, and applications. I am especially interested in trying to extend known results for curves to varieties of higher dimension.

I am interested in diophantine questions on the density of rational points –in the usual sense of algebraic varieties, as well as in problems for certain kinds of non-algebraic sets. For example, results showing that rational points are scarce (in a suitable sense) on the graph of a transcendental real analytic function –and analogous problems in higher dimensions. These problems have connections to transcendental number theory.

Research Themes

• Number Theory