Ohio State University 

   Recent papers

  1. O. Costin, M Huang and W Schlag, On the spectral properties of L± in three dimensions, Nonlinearity 25, pp. 125-164 (2012)  .arXiv

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  3. O. Costin, H. Parkh and Y. Takei, Borel summability of the heat equation with variable coefficients, J. Diff. Eq. Volume 252, 4, pp.  3076-3092 (2012).

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  5. O. Costin, M. Huang and F.  Fauvet, Global behavior of solutions of nonlinear ODEs: first order equations.  Int Math Res Notices first published online October 31, 2011 doi:10.1093/imrn/rnr203

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  7. Semiclassical low energy scattering for one-dimensional Schrödinger operators with exponentially decaying potentials (with R Donninger, W Schlag and S Tanveer) to appear in Ann. Inst. Henri Poincaré .arXiv

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  9. Global behavior of solutions of nonlinear ODEs: first order equations (with M. Huang and F. Fauvet), to appear in IMRN .arXiv

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  11. Gamow vectors and Borel summability in a class of quantum systems (with M Huang) J. Stat. Phys, Vol. 144, Number 4, pp. 846-871 (2011) Springer link, free access

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  13. Geometric construction and analytic representation of Julia sets of polynomial maps (with M. Huang) Nonlinearity 24 (2011), no. 4, 1311--1327 .arXiv

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  15. Integral equation representation and longer time existence solutions of 3-d Navier-Stokes (With G. Luo and S. Tanveer) Comm. Contemp. Math, 13 (3), pp 407-462 (2011) ArXiv

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  17. Boundary blow-up solutions in the unit ball : asymptotics, uniqueness and symmetry (with  L. Dupaigne) J. Differential Equations 249 (2010), no. 4, 931--964. arXiv

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  19. Ionization of Coulomb systems in ℝ3 by time periodic forcing of arbitrary size (with J. L. Lebowitz and S. Tanveer,  Comm. Math. Phys. 296 (2010), no. 3, 681--738 Arxiv)

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  21. Exact results for ionization of model atomic systems (with  J.L. Lebowitz, C. Stucchio and S. Tanveer, J. Math. Phys., 51, 1 (2010). pdf

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  23. Resurgence of the fractional polylogarithms (with S. Garoufalidis) , Math. Res. Lett. 16 (2009), no. 5, 817--82. arXiv

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  25. Short time existence and Borel summability in the Navier-Stokes equation in ℝ3 (with S. Tanveer). Comm. Partial Differential Equations 34 (2009), no. 7-9, 785--817 pdf

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  27. Semiclassical analysis of low and zero energy scattering for one dimensional Schrodinger operators with inverse square potentials (with  W. Schlag, W. Staubach,  & S. Tanveer, J. Functional Analysis, special issue dedicated to Paul Malliavin, 255, (2008). arXiv

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  29. Behavior of lacunary series at the natural boundary (with M. Huang, Advances in Mathematics 222 (2009) 1370–1404) Elsevier link  pdf

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  31. Ionization in damped harmonic fields (with M. Huang and Z. Qiu, J. Phys A: Math. Theor, 42 (2009))  ArXiV link    J. Phys A link  

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  33. An Integral equation Approach to Smooth 3-D Navier-Stokes Solution (with G. Luo and S. Tanveer, Physica Scripta T 132, 2008).

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  35. Resurgence of the Euler-Maclaurin summation formula (with S. Garoufalidis, Annales de l' Institut Fourier 58  893-914 (2008pdf

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  37. Nonlinear Stokes phenomena in first or second order differential equations (Algebraic Analysis of Differential Equations, T. Aoki, H. Majima, Y. Takei & N. Tose (Eds.), Springer (2008)) pdf

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  39. Ionization in a 1-dimensional dipole model (with J. L. Lebowitz and C. Stucchio),   Reviews in Mathematical Physics, 20 No: 7 , pp. 835-872 (2008) pdf

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  41. Sharp Hardy-Leray inequality for axisymmetric divergence-free fields (with V. Maz'ya,)  Calc. Var. Partial Differential Equations 32 (2008), no. 4,pdf

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  43. Divergent expansions, Borel summability and the 3-D  Navier-Stokes Equation (With G. Luo and S. Tanveer, Phil. Trans. R. Soc. A 366, pp 2775-2788 (2008)pdf.

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  45. Resurgence of the Kontsevitch-Zagier power series (with S. Garoufalidis, to appear in Annales de l'Institut Fourier) pdf

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  47. Global  reconstruction of analytic functions from local expansions and a new generalmethod of converting sums into integrals (submitted)  pdf

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  49. On the proof of universality for orthogonal and symplectic ensembles in random matrix theory (with P. Deift and D. Gioev J. Stat. Phys. 129 (2007), no. 5-6, 937--948) pdf

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Part of the recent research was supported by the NSF awards DMS-0103807, DMS-0100495, DMS-0406193 and DMS-0600369 and a Guggenheim fellowship.

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