Ben's math page

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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 Vafa-Witten invariant, 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 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!