Bjorn Mikhail Poonen

Distinguished Professor in Science. Number theorist and algebraic geometer.  Developed methods for finding the rational number solutions to polynomial equations, and methods for proving that certain such equations have no solutions.  Contributions also to problems on the borderline between logic and number theory, including proofs that certain problems in number theory and algebraic geometry are undecidable. Contributions to fundamental problems in arithmetic geometry include his Annals of Mathematics article with Michael Stoll (1999) on the Cassels-Tate pairing, with its surprising examples of non-alternating such pairings; his Inventiones Mathematicae article (1999) proving a theorem for points on subvarieties of abelian varieties that generalizes both the Mordell-Lang and the Bogolomov conjectures; and his related article with José Felipe Voloch on the existence of rational points on subvarieties X of an abelian variety defined over a global function field, in which they show that the Brauer-Manin obstruction is the only barrier to the existence of rational points on X. Publications of a purely algebraic-geometric nature include his Annals of Mathematics article on Bertini theorems over finite fields and several papers exploring connections between logic and number theory, such as one on the Diophantine definability of rings of integers in number fields.