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Alexei Oblomkov

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I am an Instructor in the Department of Mathematics at Princeton University.
My research interests include representation theory, algebraic geometry and related areas of mathematical physics.

  • CV
  • List of publications with abstracts

    Papers and preprints:


    Algeraic Geometry: Gromov-Witten and Donaldson-Thomas invariants


  • Quantum cohomology of the Hilbert scheme of points on $A_n$-resolutions, (with D. Maulik), in preparation.
  • Donaldson-Thomas theory of $A_n\times\mathbb{P}^1$ (with D. Maulik), in preparation.
  • Gromov-Witten/Donaldson-Thomas correspondences for toric threefolds (with D. Maulik, A. Okounkov and R. Pandharipande), in preparation.

    Noncommutative geometry: noncommutative surfaces


  • Double affine Hecke algebras of rank 1 and affine cubic surfaces, IMRN, (2004), no. 18, 877--912 ps
  • 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 ps
  • Quantization and orbifold cohomology (with P. Etingof), 171--182, Contemp. Math., 417, Amer. Math. Soc., Providence, RI, 2006. ps

    Representation theory: Hecke algebras and special functions


  • A Lie algebra construction of Generalized double affine Hecke algebras (with P. Etingof, S. Loktev, L. Rybnikov), in preparation.
  • Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products (with P. Etingof, W. L. Gan, V. Ginzburg), to appear in Publications mathematiques de l'IHES ps .
  • Deformed Harish-Chandra homomorphism for the cyclic quiver, Math. Res. Lett. 14 (2007), no. 3, 359--372 ps .
  • Generalized double affine Hecke algebras of higher rank, (with W. L. Gan and P. Etingof), J. Reine Angew. Math. 600 (2006), 177--201. ps .
  • The double affine Hecke algebras and Calogero-Moser spaces, Represent. Theory 8 (2004), 243--266, ps ,
  • Vector valued spherical function and Macdonald-Koornwinder polynomials, (with J. Stokman), Compos. Math. 141 (2005), no. 5, 1310--1350. ps
  • Heckman-Opdam's Jacobi polynomials for the $BC_n$ root system and generalized spherical functions , Adv. Math., 186 (2004), no. 1, 153--180 ps .
  • Finite dimensional representations of double affine Hecke algebra of rank $1$, (with E.Stoica), submitted ps

    Mathematical physics: integrable systems and inverse scattering problems


  • Laplace transformations and spectral theory of two-dimensional semi-discrete and discrete hyperbolic Schroedinger operators, (with A. Penskoi), IMRN, ps .
  • Generalized Lame operators, (with P. Etingof and O. Chalykh), Communications in Math. Physics. 239 (2003), no 1-2, 115--153 ps
  • The isoenergy spectral problem for multidimensional difference operators, (Russian) Funktsional. Anal. i Prilozhen. 36 (2002), no. 2, 45--61; translation in Funct. Anal. Appl. 36 (2002), no. 2, 120--133 ps
  • On the spectral properties of two classes of difference periodic operators, (Russian) Mat. Sb. 193 (2002), no. 4, 87--112; translation in Sb. Math. 193 (2002), no. 3-4, 559--584 ps
  • Difference operators on two-dimensional regular lattices, (Russian) Teoret. Mat. Fiz. 127 (2001), no. 1, 34--46; translation in Theoret. and Math. Phys. 127 (2001), no. 1, 435--445 ps
  • Two-dimensional algebro-geometric difference operators, (with A. Penskoi) J. Phys. A 33 (2000), no. 50, 9255--9264 ps
  • Harmonic oscillator and Darboux transformations in many dimensions, (with O. Chalykh), Phys. Lett. A 267 (2000), no. 4, 256--264 ps
  • Monodromy-free Schrodinger operators with quadratically increasing potential, (Russian) Teoret. Mat. Fiz. 121 (1999), no. 3, 374--386; translation in Theoret. and Math. Phys. 121 (1999), no. 3, 1574--1584 ps
  • Integrability of some quantum systems associated with the root system $B_2$, (Russian) 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 ps

    Projective algebraic geometry


  • 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, ps

    Current Teaching

    Advanced Multivariable Calculus (MAT203)
    Department of Mathematics
    Princeton University
    Office 607, Fine Hall
    Washington Road
    Princeton, NJ 08544
    Phone: (617) 669-2751
    e-mail: oblomkov at math dot princeton dot edu