My core research areas are in Analysis (Complex Analysis, PDE, potential theory, asymptotics), but what I really love are well-motivated problems that are simple to state.
Random Manifolds
Complex Zeros of Harmonic Functions
Univalent Harmonic Mappings
Free Boundaries
Operator Theory
Analytic Combinatorics
Coauthors: Antonio Auffinger, Saugata Basu, Steven R. Bell, Robert A. Bridges, Daoud Bshouty, Joshua N. Cooper, Omar Eldaghar, Michael Epstein, Alexandre Eremenko, Timothy Ferguson, Matthew Fleeman, Yan V. Fyodorov, Boris Hanin, Jonathan Hauenstein, Lavi Karp, Charles R. Keeton, Dmitry Khavinson, Jessica Khera, Seung-Yeop Lee, Antonio Lerario, Dhagash Mehta, Stephen Melczer, Brendan Nagle, Chris Peterson, Koushik Ramachandran, Hermann Render, Razvan Teodorescu, Vilmos Totik, Allen Weitsman. (my Erdos number is 2)