My work is in Algebraic Geometry. My focus is on singularities and the effect they have on the local and global geometry of varieties. Among my interests are topics connected with higher-dimensional birational geometry (singularities of pairs, multiplier ideals), topology (Milnor fibrations, local systems), number theory (Igusa local zeta functions), representation theory (D-modules), combinatorics (hyperplane and subspace arrangements), commutative algebra (test ideals), differential geometry (geometric stability), and physics (string theory). My work has been sponsored by NSF, NSA, Simons Foundation, and the H.J. Kenna endowment.
I am a private pilot and support AOPA.