Simons Postdoctoral Fellow
I'm an algebraic geometer. Mostly I study Hilbert schemes of points on plane curves. These can be used to count nodal curves, to study certain subtle aspects of the cohomology of some integrable systems, and conjecturally to capture the Khovanov-Rozansky homology of the links of the singularities of the curves. Some of these applications serve as contact points with ideas from high energy physics.
| Refined curve counting on complex surfaces
with Lothar Göttsche.
| Torus knots and the rational DAHA
with Alexei Oblomkov, Jacob Rasmussen, and Eugene Gorsky.
| On the Göttsche Threshold
with Steven Kleiman.
| The Hilbert scheme of a plane curve singularity and the
HOMFLY homology of its link
with Alexei Oblomkov and Jacob Rasmussen; and with an appendix by Eugene Gorsky.
| Large N duality, lagrangian cycles, and algebraic knots
with Duiliu Emanuel Diaconescu and Cumrun Vafa.
to appear in Comm. Math. Phys.
| A support theorem for Hilbert schemes of planar curves
with Luca Migliorini.
To appear in J. Eur. Math. Soc.
| A short proof of the Göttsche conjecture
with Martijn Kool and Richard Thomas.
Geometry and Topology 15 (2011), 397-406.
| Hilbert schemes of points on a locally planar curve and the
Severi strata of its versal deformation
Compositio Mathematica 148.2 (2012), 531-547.
| The Hilbert scheme of a plane curve singularity and the HOMFLY polynomial of its link
with Alexei Oblomkov
Duke Mathematical Journal 161.7 (2012), 1277-1303.