My primary research interest is gauge theory on four-dimensional manifolds.
This involves a nice mix of mathematical physics and geometric analysis, with
connections to algebraic geometry.
My current objective is to establish existence of the conjectural
which should associate a modular form to each smooth four-manifold.
For more details, see
I am also studying (ir)rationality of Chern-Simons invariants for
flat connections on three-manifolds.
Here is my thesis on Some Analytic Aspects of Vafa-Witten Twisted N=4 Supersymmetric Yang-Mills Theory
I co-organized a reading seminar to learn quantum field
The Fall 2008 graduate geometry seminar was about moduli spaces.
This moduli spaces wiki houses our notes.
A few years back I gave a few undergraduate talks about visualizing
Mollify that Peano curve!