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 01003-9305
USA

Office: LGRT 1238
Tel: (++1)-413-545-2857
Fax: (++1)-413-545-1801
email: email


Photo
CV

Current Partial Support

NSF CAREER grant DMS-1352398

Current Teaching

Introduction to Linear Algebra 235

REU program

Summer 2017 <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 01003-9305
USA

Office: LGRT 1238
Tel: (++1)-413-545-2857
Fax: (++1)-413-545-1801
email: email


Photo
CV

Current Partial Support

NSF CAREER grant DMS-1352398

Current Teaching

Introduction to Linear Algebra 235

REU program

Summer 2017

Alexei Oblomkov

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

Office: LGRT 1238
Tel: (++1)-413-545-2857
Fax: (++1)-413-545-1801
email: email


Photo
CV

Current Partial Support

NSF CAREER grant DMS-1352398

Current Teaching

Introduction to Linear Algebra 235

REU program

Summer 2017

Papers and preprints

  1. Homology of homogeneous Affine Springer Fibers in type $A$ (with Z. Yun), in preparation.
  2. GW/PT correspondence with descendents (with A. Okounkov and R. Pandharipande), in preparation.
  3. Homology of Coxeter links (with L. Rozansky).
  4. Affine Braid group, JM elements and knot homology (with L. Rozansky) to appear in Transformation Groups.
  5. Knot Homology and sheaves on the Hilbert scheme of points on the plane (with L. Rozansky), submitted.
  6. 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.
  7. Geometric representations of graded and rational Cherednik algebras, (with Z. Yun), Adv. Math. 292 (2016), 601--706.
  8. Torus knots and the rational DAHA, (with E. Gorsky; J. Rasmussen; V. Shende), Duke Math. J. 163 (2014), no. 14, 2709--2794.
  9. On stable Khovanov homology of torus knots, (with E. Gorsky; J. Rasmussen), Exp. Math. 22 (2013), no. 3, 265--281.
  10. 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), to appear in Geometry and Topology.
  11. 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.
  12. Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds, (with D. Maulik; A. Okounkov; R. Pandharipande), Invent. Math. 186 (2011), no. 2, 435–479.
  13. Donaldson-Thomas theory of $ A_n\times P^1$, (with D. Maulik), Compos. Math. 145 (2009), no. 5, 1249--1276.
  14. Quantum cohomology of the Hilbert scheme of points on $A_n$-resolutions, (with D. Maulik), JAMS, 22 (2009), no. 4, 1055-1091.
  15. Finite dimensional representations of the double affine Hecke algebra of rank 1, (with E. Stoica), J. Pure Appl. Algebra 213 (2009), no. 5, 766--771.
  16. A Lie-theoretic construction of spherical symplectic reflection algebras, (with P. Etingof; S. Loktev; L. Rybnikov), Transform. Groups, 13 (2008), no. 3-4, 541--556.
  17. Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products, (with P. Etingof, V. Ginzburg, W. L. Gan), Publ. Math. de l'IHES, no. 105 (2007), 91--155.
  18. Deformed Harish-Chandra homomorphism for the cyclic quiver, Math. Res. Lett, 14 (2007), no. 3, 359--372.
  19. 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, 749--796.
  20. Quantization, orbifold cohomology, and Cherednik algebras, (with P. Etingof), Jack, Hall-Littlewood and Macdonald polynomials, 171--182, Contemp. Math., 417, Amer. Math. Soc., Providence, RI, 2006.
  21. Generalized double affine Hecke algebras of higher rank, (with P. Etingof, W. L. Gan), J. Reine Angew. Math. 600 (2006), 177--201.
  22. Vector valued spherical functions and Macdonald-Koornwinder polynomials, (with J. Stokman), Compos. Math. 141 (2005), no. 5, 1310--1350.
  23. Laplace transformations and spectral theory of two-dimensional semidiscrete and discrete hyperbolic Schrödinger operators, (with A. Penskoi), Int. Math. Res. Not. 2005, no. 18, 1089--1126.
  24. Double affine Hecke algebras and Calogero-Moser spaces, Represent. Theory 8 (2004), 243--266.
  25. Heckman-Opdam's Jacobi polynomials for the $BC_n$ root system and generalized spherical functions, Adv. Math. 186 (2004), no. 1, 153--180.
  26. Double affine Hecke algebras of rank 1 and affine cubic surfaces, Int. Math. Res. Not. 2004, no. 18, 877--912.
  27. Generalized Lame operators, (with O. Chalykh; P. Etingof), Comm. Math. Phys. 239 (2003), no. 1-2, 115--153.
  28. The isoenergy spectral problem for multidimensional difference operators, Funktsional. Anal. i Prilozhen. 36 (2002), no. 2, 45--61, 96; translation in Funct. Anal. Appl. 36 (2002), no. 2, 120--133.
  29. On the spectral properties of two classes of difference periodic operators, Mat. Sb. 193 (2002), no. 4, 87--112; translation in Sb. Math. 193 (2002), no. 3-4, 559--584.
  30. Difference operators on two-dimensional regular lattices, Teoret. Mat. Fiz. 127 (2001), no. 1, 34--46; translation in Theoret. and Math. Phys. 127 (2001), no. 1, 435--445.
  31. Two-dimensional algebro-geometric difference operators. (with A. Penskoi), J. Phys. A 33 (2000), no. 50, 9255--9264.
  32. Harmonic oscillator and Darboux transformations in many dimensions, (with O. Chalykh), Phys. Lett. A 267 (2000), no. 4, 256--264.
  33. Monodromy-free Schrodinger operators with quadratically increasing potential, Teoret. Mat. Fiz. 121 (1999), no. 3, 374--386; translation in Theoret. and Math. Phys. 121 (1999), no. 3, 1574--1584.
  34. Integrability of some quantum systems associated with the root system $B_2$, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1999, , no. 2, 6--9, 72; translation in Moscow Univ. Math. Bull. 54 (1999), no. 2, 5--8
  35. 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.