I am an algebraic geometer and currently a postdoc at UC Berkeley.
At the moment I am mostly interested in algebraic stacks. A brief list of interests include:
Moduli Chow and Hilbert schemes, Hilbert stacks, higher-dimensional moduli, coarse quotients, …
Algebraic spaces and stacks (foundational).
Riemann-Zariski spaces, valuation theory, rigid geometry
Two-dimensional sheaf theory.
minimal model program, multiplier ideal sheaves
Commutative algebra (from a geometric viewpoint): divided powers, seminormality, weak normality, ideal closures such as tight closure, absolute flat (and perfect) rings