Nathan Grieve, Acadia University
"On Schmidt's Subspace Theorem, Vojta's height inequalities and algebraic points in projective varieties: recent developments and progress"
I will report on a collection of recent results and ongoing work that surround extensions and applications of Schmidt's Subspace Theorem and Vojta's height inequalities. As two examples: (i) It is of interest to understand the qualitative features of Diophantine exceptional sets; (ii) It is of interest to understand the extent to which algebraic points of a given bounded degree in a given general type projective variety are not-Zariski dense. As I will explain, there are several logically equivalent points of departure for these results. They build on a collection of my past contributions in addition to work of many others.