Alexei Oblomkov

Alexei Oblomkov

Professor

Personal Webpage

Office:

LGRT 1235H

Phone:

413-545-2857

Email:

Office Hours

M 11-12:15 LGRT 1235H; TuTh 11:15-12

Current Courses

Complex Variables
MATH 421.1

TuTh 10:00 am - 11:15 am

Education

Ph.D. MIT, 2005

Mailing Address

Department of Mathematics and Statistics
Lederle Graduate Research Tower
University of Massachusetts
710 N. Pleasant Street
Amherst, MA 01003-9305

Research Interests

Representation Theory, Algebraic Geometry and Mathematical Physics

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.

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.

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Office Hours

Current Courses

Education

Mailing Address

Department of Mathematics and Statistics