| Main | Contact | Math |
ResearchMy primary research interest is gauge theory on three- and four-dimensional manifolds. This involves a nice mix of mathematical physics and geometric analysis, with connections to algebraic geometry and number theory.I am currently studying questions related to the (ir)rationality of Chern-Simons invariants for flat connections on three-manifolds. See my preprint with Yuta Nozaki and Masaki Taniguchi: The homology cobordism group is not generated by graph homology 3-spheres. In my doctoral thesis, I studied analytic aspects of the Vafa-Witten equations, toward a construction of the conjectural Vafa-Witten invariants. These invariants have since been constructed for smooth complex projective surfaces by Tanaka and Thomas. The general smooth four-manifold case remains open, despite substantial progress by Clifford Taubes and others. For background on my thesis work, see Teaching
MiscellaneousI 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! |
