Teaching
Research
My primary research interest is gauge theory on fourdimensional 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
VafaWitten invariant,
which should associate a modular form to each smooth fourmanifold.
For more details, see
I am also studying (ir)rationality of ChernSimons invariants for
flat connections on threemanifolds.
Here is my thesis on Some Analytic Aspects of VafaWitten Twisted N=4 Supersymmetric YangMills Theory
Miscellaneous
I coorganized a reading seminar to learn quantum field
theory.
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
funny functions.
Mollify that Peano curve!
