I also applied - do we know if anyone has heard back from them yet? I know math and philosophy acceptances are already out, so I don't know if I should despair. I got into Irvine LPS though, so I'm happy I can go somewhere to pursue my interests. I have broad interests, but with respect to Berkeley, I'm particularly interested in doing set theory, with an eye towards exploring philosophical questions about the justification for additional axioms (like large cardinals and reflection principles) and answering questions like the Continuum hypothesis that are independent of the axioms. (Unfortunately, Hugh Woodin recently left to Harvard though, but they still have John Steel...) I'm also interested in model theory/computability theory, more general quesstions in the philosophy of logic/mathematics, and lastly formal epistemology.