Harmonic Analysis; Partial Differential Equations:
Solvability of boundary value problems (Dirichlet, Neumann, Regularity)
Elliptic and Parabolic equations, systems and complex valued PDEs
Partial differential equations with rough coefficients on domains with limited regularity
Connections between harmonic analysis and solvability of PDEs (elliptic and parabolic measures, singular integral operators)
Applications in Geometry, Physics and Mechanics
Current and Recent PhD Students
PhD students (1st supervisor): Josef Kirsch (2008--2012), Luke Dyer (2014-2018).
Post-docs: Treven Wall (2006--2008), Nicholas Longo (2008--2010), Sukjung Hwang (2012--2015)
Recent Conference and Workshop Involvement
Main organizer of ICMS workshop "Harmonic analysis and PDEs" (50 participants), July 2015, Edinburgh.
Co-organizer of mini-symposium in Analysis at the Joint conference of Edinburgh Mathematical Society and Catalan Mathematical Society, May 2015, Barcelona, Spain.
IAS/PMCI Research Program in Mathematics, Park City, USA, July 2018
Interactions of Harmonic Analysis and Operator Theory, Birmingham
ICMAT Workshop on Harmonic Analysis, Partial Differential Equations and and Geometric Measure Theory, Madrid
Clay Mathematics Institute, Cambridge MA, Liftoff Fellow, summer 2001 Department of Mathematics, Cornell University, Assistant Professor, 2001-2004 Department of Mathematics, Brown University, Assistant Professor, 2004-2005
Ph.D University of North Carolina, Chapel Hill NC (USA) (2001)
Ph.D Comenius University Bratislava (Slovakia) (2000)