2012 Ribenboim Prize in Number Theory

This year's recipient of the Ribenboim prize in number theory is Dragos Ghioca from the University of British Columbia.

Dragos Ghioca is one of the most energetic, productive, and influential researchers of his generation in the field of arithmetic algebraic geometry. His research is at the interplay of Number Theory, Algebraic Geometry and Discrete Dynamical Systems. Within the seven years since his PhD from Berkeley Dragos has established himself as one of the leading experts in two very important areas of current research: the theory of Drinfeld modules and the field of arithmetic dynamics.

In a series of papers, Dragos proves Drinfeld module analogues of classical theorems from Diophantine geometry. Such proofs are generally not direct translations of the classical proofs; they require significant new ideas, not to mention a deep understanding of the theory. Among Dragos’s results are Drinfeld module analogues of the Mordell–Lang theorem, Lehmer’s conjecture, the Mordell–Weil theorem, equidistribution results for torsion points, and estimates for integral points.

Recently Dragos has turned to the comparatively new field of arithmetic dynamics. The starting point is an algebraic variety $X$ and a (non-linear) self-map $\phi : X \rightarrow X.$ Classical (discrete) dynamics is the study of orbits $O_\phi(x) = \{x, \phi(x), \phi^2(x), . . .\}$ of points $x \in X$ under iteration of $\phi$. Arithmetic dynamics is the study of arithmetic properties of orbits. The subject is driven by a number of deep conjectures, many of them dynamical analogues of classical theorems and conjectures in arithmetic geometry, such as the celebrated Mordell-Lang conjecture. Here Dragos and his co-workers found fundamental results, for instance, a surprising counterexample to a conjecture of Zhang. This led to reformulations and also to some positive results, i.e. proofs of certain other natural analogues which survived the counterexample.

The prize presentation and lecture will happen during CNTA XII in Lethbridge, on Wednesday June 20 at 9:00 AM in PE250.