Manjul Bhargava's new field of arithmetic invariant theory is a perfect example of a new grand project. It began with Manjul's doctoral thesis, in which he presented a completely new view of Gauss's composition law for binary quadratic forms in a way that led to generalizations. This led to a series of papers(mostly in the Annals of Mathematics) on a plethora of generalizations , in particular to cubic forms and beyond, with a general framework coming from representation theory.
In addition to being intrinsically interesting, this has led to new results on counting quadratic rings, cubic rings, etc, which has in turn led to whose crowning achievement is an important new results result on the Birch and Swinnerton-Dyer conjecture (see the work of c.f. Bhargava and Shankar). There is much more to research in the theory, and numerous people (including some of his students) have found numerous manifold connections with other areas of math, such as knot theory and algebraic geometry.
See here for an overview of Manjul's work.
See here for some notes from a seminar at Princeton that shows the vast reach of this theory.
