LGRT 1235H

I am interested in geometric aspects of Representation Theory. I am also interested in the geometry of moduli spaces that appear in Mathematical Physics: moduli space of sheaves (Donaldson-Thomas and Pandharipande-Thomas theories), moduli spaces of stable maps (Gromov-Witten theory), Nakajima quiver varieties, Springer fibers, Hilbert schemes of points on a singular curve. Recently, I was studying various connections between the enumerative invariants of the spaces from the previous list and the topological invariants.


Ph.D. MIT, 2005


Representation Theory, Algebraic Geometry and Mathematical Physics

Selected Publications

  • Quantum cohomology of the Hilbert scheme of points on A_n-resolutions. (with D. Maulik) J. Amer. Math. Soc. 22 (2009), no. 4, 1055--1091.
  • Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds, (with D. Maulik; A. Okounkov; R. Pandharipande), Invent. Math. 186 (2011), no. 2, 435–479.
  • The Hilbert scheme of a plane curve singularity and the HOMFLY polynomial of its link, (with V. Shende), Duke Math. J. Volume 161, Number 7 (2012), 1277--1303.
  • The Hilbert scheme of a plane curve singularity and the HOMFLY homology of its link, (with J. Rasmussen; V. Shende and appendix by E. Gorsky), Geometry and Topology. 22 (2018), no. 2, 645–691.
  • Geometric representations of graded and rational Cherednik algebras, (with Z. Yun), Adv. Math. 292 (2016), 601--706.
  • GW/PT correspondence with descendents (with A. Okounkov and R. Pandharipande), Communications in Mathematical Physics, 2019.
  • Knot Homology and sheaves on the Hilbert scheme of points on the plane (with L. Rozansky), Selecta Math. (N.S.) 24 (2018), no. 3, 2351--2454.