Robert M. Solovay's current project in the foundations of mathematics has two parts, one in set theory and one in models of arithmetic. The work in set theory will attempt to show that some unresolved questions concerning C*-algebras are actually independent of the customary axioms of set theory, the so-called Zermelo-Fraenkel axioms. This would mean that they could be settled only by adopting additional axioms, such as the desired answers themselves. Since C*-algebras are an important object of study in modern analysis, this part of the project would have a wider audience that most projects in foundations. The other part, concerning models of arithmetic, is somewhat more technical, likely to have an enthusiastic but more restricted audience.
