# Alexei Oblomkov

Professor

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.

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Education

Ph.D. MIT, 2005

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RESEARCH INTERESTS

Representation Theory, Algebraic Geometry and Mathematical Physics

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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.