Alexei Oblomkov's home page
Alexei Oblomkov
Department of Mathematics and Statistics
University of Massachusetts
Lederle Graduate Research Tower
710 North Pleasant Street
Amherst, MA 010039305
USA
Office: LGRT 1238
Tel: (++1)4135452857
Fax: (++1)4135451801
email: email
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Current Partial Support
NSF grant DMS2200798
NSF FGR grant DMS1760373
Current Teaching
MATH 797RT: Introduction to Representation Theory.
Conferences and activities
Categorical braid group actions and categorical representation theory, June 14June 18, 2021.
AIM research community: Link homology
Papers and preprints
 Generic curves and noncoprime Catalans
(with E. Gorsky and M. Mazin ).
 The affine Springer fiber  sheaf correspondence
(with E. Gorsky and O. Kivinen ).
 Soergel bimodules and matrix factorizations
(with L. Rozansky).
 Virasoro constraints for stable pairs on toric 3folds
(with M. Moreira, A. Okounkov, R. Pandharipande).
 A compactification of the moduli space of marked vertical lines in $\mathbb{C}^2$
(with N. Bottman).
 Dualizable link homology
(with L. Rozansky).
 Notes on matrix factorizations and knot homology
.
 EGL formula for DT/PT theory of local curves
.
 3D TQFT and HOMFLYPT homology
(with L. Rozansky).
 Categorical Chern character and braid groups
(with L. Rozansky).
 Symplectic involutions of $K3^{[n]}$ type and Kummer $n$ type manifolds
(with L. Kamenova and G. Mongardi).
 GW/PT correspondence with descendents
(with A. Okounkov and R. Pandharipande), Communications in Mathematical Physics, 2019.
 Affine Schubert calculus and double coinvariants
(with E. Carlsson).
 A categorification of a cyclotomic Hecke algebra
(with L. Rozansky).
 The cohomology ring of certain compactified Jacobians
(with Z. Yun).
 Homology of Coxeter links
(with L. Rozansky).
 Affine Braid group, JM elements and knot homology
(with L. Rozansky), Transformation Groups, 2018, 14 pages.
 Knot Homology and sheaves on the Hilbert scheme of points on the plane
(with L. Rozansky), Selecta Math. (N.S.) 24 (2018), no. 3, 23512454.
 Lectures on knot homology
(with S. Nawata), Proceedings of "Workshop on Physics and Mathematics of Link Homology", at Centre de Recherches Mathematiques, Universite de Montreal, 2016.

Geometric representations of graded and rational Cherednik algebras,
(with Z. Yun), Adv. Math. 292 (2016), 601706.

Torus knots and the rational DAHA,
(with E. Gorsky; J. Rasmussen; V. Shende), Duke Math. J. 163 (2014), no. 14, 27092794.

On stable Khovanov homology of torus knots,
(with E. Gorsky; J. Rasmussen), Exp. Math. 22 (2013), no. 3, 265281.

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..

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), 12771303.

GromovWitten/DonaldsonThomas correspondence for toric 3folds,
(with D. Maulik; A. Okounkov;
R. Pandharipande), Invent. Math. 186 (2011), no. 2, 435–479.

DonaldsonThomas theory of $ A_n\times P^1$, (with D. Maulik), Compos. Math. 145 (2009), no. 5, 12491276.

Quantum cohomology of the Hilbert scheme of points on $A_n$resolutions,
(with D. Maulik), JAMS, 22 (2009), no. 4, 10551091.

Finite dimensional representations of the double affine Hecke algebra of rank 1,
(with E. Stoica), J. Pure Appl. Algebra 213 (2009), no. 5, 766771.

A Lietheoretic construction of spherical symplectic reflection algebras,
(with P. Etingof; S. Loktev; L. Rybnikov), Transform. Groups, 13 (2008), no. 34, 541556.

HarishChandra homomorphisms and symplectic reflection algebras for wreathproducts,
(with P. Etingof, V. Ginzburg, W. L. Gan), Publ. Math. de l'IHES, no. 105 (2007), 91155.

Deformed HarishChandra homomorphism for the cyclic quiver,
Math. Res. Lett, 14 (2007), no. 3, 359372.

Generalized double affine Hecke algebras of rank 1 and quantized del Pezzo surfaces,
(with P. Etingof and E. Rains), Adv. Math. 212 (2007), no. 2, 749796.

Quantization, orbifold cohomology, and Cherednik algebras,
(with P. Etingof), Jack, HallLittlewood and Macdonald polynomials, 171182, Contemp. Math., 417, Amer. Math. Soc., Providence, RI, 2006.

Generalized double affine Hecke algebras of higher rank,
(with P. Etingof, W. L. Gan), J. Reine Angew. Math. 600 (2006), 177201.

Vector valued spherical functions and MacdonaldKoornwinder polynomials,
(with J. Stokman), Compos. Math. 141 (2005), no. 5, 13101350.

Laplace transformations and spectral theory of twodimensional semidiscrete and discrete hyperbolic Schrödinger operators,
(with A. Penskoi), Int. Math. Res. Not. 2005, no. 18, 10891126.

Double affine Hecke algebras and CalogeroMoser spaces,
Represent. Theory 8 (2004), 243266.

HeckmanOpdam's Jacobi polynomials for the $BC_n$ root system and generalized spherical functions,
Adv. Math. 186 (2004), no. 1, 153180.

Double affine Hecke algebras of rank 1 and affine cubic surfaces,
Int. Math. Res. Not. 2004, no. 18, 877912.

Generalized Lame operators,
(with O. Chalykh; P. Etingof), Comm. Math. Phys. 239 (2003), no. 12, 115153.

The isoenergy spectral problem for multidimensional difference operators,
Funktsional. Anal. i Prilozhen. 36 (2002), no. 2, 4561, 96; translation in Funct. Anal. Appl. 36 (2002), no. 2, 120133.
 On the spectral properties of two classes of difference periodic operators,
Mat. Sb. 193 (2002), no. 4, 87112; translation in Sb. Math. 193 (2002), no. 34, 559584.
 Difference operators on twodimensional regular lattices,
Teoret. Mat. Fiz. 127 (2001), no. 1, 3446; translation in Theoret. and Math. Phys. 127 (2001), no. 1, 435445.
 Twodimensional algebrogeometric difference operators.
(with A. Penskoi), J. Phys. A 33 (2000), no. 50, 92559264.
 Harmonic oscillator and Darboux transformations in many dimensions,
(with O. Chalykh), Phys. Lett. A 267 (2000), no. 4, 256264.
 Monodromyfree Schrodinger operators with quadratically increasing potential,
Teoret. Mat. Fiz. 121 (1999), no. 3, 374386; translation in Theoret. and Math. Phys. 121 (1999), no. 3, 15741584.
 Integrability of some quantum systems associated with the root system $B_2$,
Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1999, , no. 2, 69, 72; translation in Moscow Univ. Math. Bull. 54 (1999), no. 2, 58
 On congruences of lines of order one in $\mathbb{P}^3$, (with A. Inshakov,
S. L'vovski and F. Zak),
preprint 1999, Independent University of Moscow.