Scholars@Duke

• Background
• 

  Education, Training, & Certifications

  • Ph.D., California Institute of Technology 1997
• 

  Academic Positions Outside Duke

  • Edgar Odell Lovett Professor of Mathematics, Rice University. 2017
  • Professor, Rice University. 2014 - 2016
  • Professor, University of Wisconsin-Madison. 2005 - 2014
  • Associate Professor, University of Wisconsin-Madison. 2002 - 2005
  • Assistant Professor, University of Chicago. 1999 - 2002
  • Dickson Instructor , University of Chicago. 1997 - 1999
  • Postdoc, Mathematical Sciences Research Institute. 1996 - 1997
• Recognition
• 

  In the News

  • OCT 5, 2017

    Alexander Kiselev: Mixing It Up
• 

  Awards & Honors

  • 12th Brooke Benjamin Lecture. Oxford University. 2019
  • International Congress of Mathematicians 2018, Invited Speaker, Partial Differential Equations Section. International Mathematical Union. 2017
  • Avron Douglis Memorial Lecture. University of Maryland . 2014
  • Guggenheim Fellowship. John Simon Guggenheim Foundation . 2012
  • Plenary Speaker at AMS sectional meeting. AMS program committee. 2009
  • Invited Speaker at International Congress in Mathematical Physics. International Association of Mathematical Physics. 2006
  • NSF Career award. NSF. 2002
  • Alfred P. Sloan Research Fellowship. A.P. Sloan Foundation . 2001
• Expertise
• 

  Subject Headings

  • Biology--Mathematical models
  • Fluid mechanics
  • Reaction-diffusion equations
  • Spectral theory (Mathematics)
• Research
• 

  Selected Grants

  • Regularity, blow up and mixing in fluids awarded by  National Science Foundation 2018 - 2020
• 

  Fellowships, Supported Research, & Other Grants

  • Regularity, Blow UP, and Mixing in Fluids awarded by NSF 2017 - 2020
  • Topics in Applied PDE awarded by NSF 2014 - 2018
• Publications & Artistic Works
• 

  Selected Publications

  • Academic Articles

    • Kiselev, A., and C. Li. “Global regularity and fast small-scale formation for Euler patch equation in a smooth domain.” Communications in Partial Differential Equations 44, no. 4 (April 3, 2019): 279–308. https://doi.org/10.1080/03605302.2018.1546318.
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    • Do, T., A. Kiselev, and X. Xu. “Stability of Blowup for a 1D Model of Axisymmetric 3D Euler Equation.” Journal of Nonlinear Science 28, no. 6 (December 1, 2018): 2127–52. https://doi.org/10.1007/s00332-016-9340-7.
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    • Kiselev, A. “Special Issue Editorial: Small Scales and Singularity Formation in Fluid Dynamics.” Journal of Nonlinear Science 28, no. 6 (December 1, 2018): 2047–50. https://doi.org/10.1007/s00332-018-9452-3.
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    • Do, T., A. Kiselev, L. Ryzhik, and C. Tan. “Global Regularity for the Fractional Euler Alignment System.” Archive for Rational Mechanics and Analysis 228, no. 1 (April 1, 2018). https://doi.org/10.1007/s00205-017-1184-2.
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    • Kiselev, A., and C. Tan. “Finite time blow up in the hyperbolic Boussinesq system.” Advances in Mathematics 325 (February 5, 2018): 34–55. https://doi.org/10.1016/j.aim.2017.11.019.
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    • Kiselev, A., and C. Tan. “Global regularity for 1D eulerian dynamics with singular interaction forces.” Siam Journal on Mathematical Analysis 50, no. 6 (January 1, 2018): 6208–29. https://doi.org/10.1137/17M1141515.
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    • Choi, K., T. Y. Hou, A. Kiselev, G. Luo, V. Sverak, and Y. Yao. “On the Finite-Time Blowup of a One-Dimensional Model for the Three-Dimensional Axisymmetric Euler Equations.” Communications on Pure and Applied Mathematics 70, no. 11 (November 1, 2017): 2218–43. https://doi.org/10.1002/cpa.21697.
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    • Kiselev, A., Y. Yao, and A. Zlatoš. “Local Regularity for the Modified SQG Patch Equation.” Communications on Pure and Applied Mathematics 70, no. 7 (July 1, 2017): 1253–1315. https://doi.org/10.1002/cpa.21677.
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    • Kiselev, A., and X. Xu. “Suppression of Chemotactic Explosion by Mixing.” Archive for Rational Mechanics and Analysis 222, no. 2 (November 1, 2016): 1077–1112. https://doi.org/10.1007/s00205-016-1017-8.
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    • Popov, I. Y., P. A. Kurasov, S. N. Naboko, A. A. Kiselev, A. E. Ryzhkov, A. M. Yafyasov, G. P. Miroshnichenko, et al. “A distinguished mathematical physicist Boris S. Pavlov.” Nanosystems: Physics, Chemistry, Mathematics, October 25, 2016, 782–88. https://doi.org/10.17586/2220-8054-2016-7-5-782-788.
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    • Kiselev, A., L. Ryzhik, Y. Yao, and A. Zlatoš. “Finite time singularity for the modified SQG patch equation.” Annals of Mathematics 184, no. 3 (January 1, 2016): 909–48. https://doi.org/10.4007/annals.2016.184.3.7.
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    • Kiselev, A., and A. Zlatoš. “Blow up for the 2D Euler equation on some bounded domains.” Journal of Differential Equations 259, no. 7 (January 1, 2015): 3490–94. https://doi.org/10.1016/j.jde.2015.04.027.
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    • Choi, K., A. Kiselev, and Y. Yao. “Finite Time Blow Up for a 1D Model of 2D Boussinesq System.” Communications in Mathematical Physics 334, no. 3 (January 1, 2014): 1667–79. https://doi.org/10.1007/s00220-014-2146-2.
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    • Dabkowski, M., A. Kiselev, L. Silvestre, and V. Vicol. “Global well-posedness of slightly supercritical active scalar equations.” Analysis and Pde 7, no. 1 (January 1, 2014): 43–72. https://doi.org/10.2140/apde.2014.7.43.
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    • Iyer, G., A. Kiselev, and X. Xu. “Lower bounds on the mix norm of passive scalars advected by incompressible enstrophy-constrained flows.” Nonlinearity 27, no. 5 (January 1, 2014): 973–85. https://doi.org/10.1088/0951-7715/27/5/973.
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    • Kiselev, A., and V. Šverák. “Small scale creation for solutions of the incompressible two-dimensional Euler equation.” Annals of Mathematics 180, no. 3 (January 1, 2014): 1205–20. https://doi.org/10.4007/annals.2014.180.3.9.
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    • Kiselev, A., and F. Nazarov. “A simple energy pump for the surface quasi-geostrophic equation.” Nonlinear Partial Differential Equations: The Abel Symposium 2010, December 1, 2012, 175–79. https://doi.org/10.1007/978-3-642-25361-4_9.
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    • Kiselev, A., and L. Ryzhik. “Biomixing by chemotaxis and efficiency of biological reactions: The critical reaction case.” Journal of Mathematical Physics 53, no. 11 (November 27, 2012). https://doi.org/10.1063/1.4742858.
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    • Dabkowski, M., A. Kiselev, and V. Vicol. “Global well-posedness for a slightly supercritical surface quasi-geostrophic equation.” Nonlinearity 25, no. 5 (May 1, 2012): 1525–35. https://doi.org/10.1088/0951-7715/25/5/1525.
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    • Kiselev, A., and L. Ryzhik. “Biomixing by Chemotaxis and Enhancement of Biological Reactions.” Communications in Partial Differential Equations 37, no. 2 (February 1, 2012): 298–318. https://doi.org/10.1080/03605302.2011.589879.
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    • Kiselev, A. “Nonlocal maximum principles for active scalars.” Advances in Mathematics 227, no. 5 (August 1, 2011): 1806–26. https://doi.org/10.1016/j.aim.2011.03.019.
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    • Kiselev, A., and F. Nazarov. “Variation on a theme of caffarelli and vasseur.” Journal of Mathematical Sciences 166, no. 1 (March 1, 2010): 31–39. https://doi.org/10.1007/s10958-010-9842-z.
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    • Kiselev, A., and F. Nazarov. “Global regularity for the critical dispersive dissipative surface quasi-geostrophic equation.” Nonlinearity 23, no. 3 (February 1, 2010): 549–54. https://doi.org/10.1088/0951-7715/23/3/006.
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    • Berestycki, H., A. Kiselev, A. Novikov, and L. Ryzhik. “The explosion problem in a flow.” Journal D’Analyse Mathematique 110, no. 1 (January 1, 2010): 31–65. https://doi.org/10.1007/s11854-010-0002-7.
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    • Kiselev, A. “Regularity and blow up for active scalars.” Mathematical Modelling of Natural Phenomena 5, no. 4 (January 1, 2010): 225–55. https://doi.org/10.1051/mmnp/20105410.
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    • Kim, A., and A. Kiselev. “Absolutely continuous spectrum of discrete Schrödinger operators with slowly oscillating potentials.” Mathematische Nachrichten 282, no. 4 (April 1, 2009): 552–68. https://doi.org/10.1002/mana.200810754.
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    • Kiselev, A., R. Shterenberg, and A. Zlatoš. “Relaxation enhancement by time-periodic flows.” Indiana University Mathematics Journal 57, no. 5 (December 16, 2008): 2137–52. https://doi.org/10.1512/iumj.2008.57.3349.
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    • Constantin, P., A. Kiselev, L. Ryzhik, and A. Zlatoš. “Diusion and mixing in fluid flow.” Annals of Mathematics 168, no. 2 (December 1, 2008): 643–74. https://doi.org/10.4007/annals.2008.168.643.
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    • Kiselev, A., F. Nazarov, and R. Shterenberg. “Blow up and regularity for fractal burgers equation.” Dynamics of Partial Differential Equations 5, no. 3 (January 1, 2008): 211–40. https://doi.org/10.4310/DPDE.2008.v5.n3.a2.
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    • Kiselev, A., F. Nazarov, and A. Volberg. “Global well-posedness for the critical 2D dissipative quasi-geostrophic equation.” Inventiones Mathematicae 167, no. 3 (March 1, 2007): 445–53. https://doi.org/10.1007/s00222-006-0020-3.
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    • Denisov, Sergey A., and Alexander Kiselev. “Spectral properties of schrodinger operators with decaying potentials.” Edited by F. Gesztesy, P. Deift, C. Galvez, P. Perry, and W. Schlag. Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon’S 60th Birthday 76 (January 1, 2007): 565–89.
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    • Kiselev, A., and A. Zlatoš. “Quenching of combustion by shear flows.” Duke Mathematical Journal 132, no. 1 (March 15, 2006): 49–72. https://doi.org/10.1215/S0012-7094-06-13212-X.
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    • Fannjiang, A., A. Kiselev, and L. Ryzhik. “Quenching of reaction by cellular flows.” Geometric and Functional Analysis 16, no. 1 (February 1, 2006): 40–69. https://doi.org/10.1007/s00039-006-0554-y.
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    • Andrzejewski, David, Erick Butzlaff, Alexander Kiselev, and Lam Raga A. Markely. “Enhancement of combustion by drift in a coupled reaction-diffusion model.” Communications in Mathematical Sciences 4, no. 1 (2006): 213–25. https://doi.org/10.4310/cms.2006.v4.n1.a8.
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    • Berestycki, H., F. Hamel, A. Kiselev, and L. Ryzhik. “Quenching and propagation in KPP reaction-diffusion equations with a heat loss.” Archive for Rational Mechanics and Analysis 178, no. 1 (October 1, 2005): 57–80. https://doi.org/10.1007/s00205-005-0367-4.
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    • Kiselev, A., and A. Zlatoš. “On discrete models of the Euler equation.” International Mathematics Research Notices, no. 38 (August 28, 2005): 2315–39.
    • Kiselev, A. "Imbedded singular continuous spectrum for Schrödinger operators." Journal of the American Mathematical Society 18, no. 3 (July 1, 2005): 571-603.  Full Text
    • Germinet, François, Alexander Kiselev, and Serguei Tcheremchantsev. “Transfer matrices and transport for Schrödinger operators.” Annales De L’Institut Fourier 54, no. 3 (2004): 787–830. https://doi.org/10.5802/aif.2034.
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    • Constantin, P., A. Kiselev, and L. Ryzhik. “Fronts in Reactive Convection: Bounds, Stability, and Instability.” Communications on Pure and Applied Mathematics 56, no. 12 (December 1, 2003): 1781–1803. https://doi.org/10.1002/cpa.10110.
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    • Killip, R., A. Kiselev, and Y. Last. “Dynamical upper bounds on wavepacket spreading.” American Journal of Mathematics 125, no. 5 (October 1, 2003): 1165–98.
    • Vladimirova, N., P. Constantin, A. Kiselev, O. Ruchayskiy, and L. Ryzhik. “Flame enhancement and quenching in fluid flows.” Combustion Theory and Modelling 7, no. 3 (September 1, 2003): 487–508. https://doi.org/10.1088/1364-7830/7/3/303.
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    • Kiselev, A., Y. Last, and B. Simon. “Stability of singular spectral types under decaying pertubations.” Journal of Functional Analysis 198, no. 1 (February 20, 2003): 1–27. https://doi.org/10.1016/S0022-1236(02)00053-8.
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    • Christ, M., and A. Kiselev. “Absolutely continuous spectrum of Stark operators.” Arkiv for Matematik 41, no. 1 (January 1, 2003): 1–33. https://doi.org/10.1007/BF02384565.
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    • Gesztesy, F., A. Kiselev, and K. A. Makarov. “Uniqueness results for matrix-valued Schrödinger, Jacobi, and Dirac-type operators.” Mathematische Nachrichten 239–240 (August 23, 2002): 103–45. https://doi.org/10.1002/1522-2616(200206)239:1<103::AID-MANA103>3.0.CO;2-F.
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    • Christ, M., and A. Kiselev. “Scattering and wave operators for one-dimensional Schrödinger operators with slowly decaying nonsmooth potentials.” Geometric and Functional Analysis 12, no. 6 (January 1, 2002): 1174–1234. https://doi.org/10.1007/s00039-002-1174-9.
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    • Constantin, P., A. Kiselev, and L. Ryzhik. “Quenching of flames by fluid advection.” Communications on Pure and Applied Mathematics 54, no. 11 (November 1, 2001): 1320–42. https://doi.org/10.1002/cpa.3000.
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    • Kiselev, A., and L. Ryzhik. “An upper bound for the bulk burning rate for systems.” Nonlinearity 14, no. 5 (September 1, 2001): 1297–1310. https://doi.org/10.1088/0951-7715/14/5/319.
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    • Christ, M., and A. Kiselev. “WKB asymptotic behavior of almost all generalized eigenfunctions for one-dimensional Schrödinger operators with slowly decaying potentials.” Journal of Functional Analysis 179, no. 2 (February 1, 2001): 426–47. https://doi.org/10.1006/jfan.2000.3688.
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    • Christ, M., and A. Kiselev. “Maximal functions associated to filtrations.” Journal of Functional Analysis 179, no. 2 (February 1, 2001): 409–25. https://doi.org/10.1006/jfan.2000.3687.
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    • Christ, M., and A. Kiselev. “WKB and spectral analysis of one-dimensional Schrödinger operators with slowly varying potentials.” Communications in Mathematical Physics 218, no. 2 (January 1, 2001): 245–62. https://doi.org/10.1007/PL00005556.
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    • Kiselev, A., and L. Ryzhik. “Enhancement of the traveling front speeds in reaction-diffusion equations with advection.” Annales De L’Institut Henri Poincare (C) Analyse Non Lineaire 18, no. 3 (January 1, 2001): 309–58. https://doi.org/10.1016/S0294-1449(01)00068-3.
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    • Kiselev, A. "Absolutely continuous spectrum of perturbed stark operators." Transactions of the American Mathematical Society 352, no. 1 (December 1, 2000): 243-256.
    • Constantin, P., A. Kiselev, A. Oberman, and L. Ryzhik. “Bulk burning rate in passive-reactive diffusion.” Archive for Rational Mechanics and Analysis 154, no. 1 (January 1, 2000): 53–91. https://doi.org/10.1007/s002050000090.
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    • Kiselev, A., and Y. Last. “Solutions, spectrum, and dynamics for schrödinger operators on infinite domains.” Duke Mathematical Journal 102, no. 1 (January 1, 2000): 125–50. https://doi.org/10.1215/S0012-7094-00-10215-3.
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    • Kiselev, A. "An interpolation theorem related to the A.E. convergence of integral operators." Proceedings of the American Mathematical Society 127, no. 6 (December 1, 1999): 1781-1785.
    • Kiselev, A., C. Remling, and B. Simon. “Effective perturbation methods for one-dimensional Schrödinger operators.” Journal of Differential Equations 151, no. 2 (January 20, 1999): 290–312. https://doi.org/10.1006/jdeq.1998.3514.
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    • Christ, M, and Kiselev, A. "Absolutely continuous spectrum for one-dimensional Schrödinger operators with slowly decaying potentials: Some optimal results." Journal of the American Mathematical Society 11, no. 4 (October 1, 1998): 771-797.
    • Kiselev, A. “Stability of the absolutely continuous spectrum of the Schrödinger equation under slowly decaying perturbations and A.E. convergence of integral operators.” Duke Mathematical Journal 94, no. 3 (January 1, 1998): 619–46. https://doi.org/10.1215/S0012-7094-98-09425-X.
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    • Kiselev, A., Y. Last, and B. Simon. “Modified prüfer and EFGP transforms and the spectral analysis of one dimensional schrödinger operators.” Communications in Mathematical Physics 194, no. 1 (January 1, 1998). https://doi.org/10.1007/s002200050346.
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    • Kiselev, A. “Some examples in one-dimensional "geometric" scattering on manifolds.” Journal of Mathematical Analysis and Applications 212, no. 1 (August 1, 1997): 263–80. https://doi.org/10.1006/jmaa.1997.5497.
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    • Christ, M., A. Kiselev, and C. Remling. “The absolutely continuous spectrum of one-dimensional Schrödinger operators with decaying potentials.” Mathematical Research Letters 4, no. 5 (January 1, 1997): 719–23. https://doi.org/10.4310/MRL.1997.v4.n5.a9.
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    • Kiselev, A. “Absolutely continuous spectrum of one-dimensional Schrödinger operators and Jacobi matrices with slowly decreasing potentials.” Communications in Mathematical Physics 179, no. 2 (December 1, 1996): 377–400.
    • Kiselev, A. A., and I. Y. Popov. “Indefinite metric and scattering by a domain with a small hole.” Mathematical Notes 58, no. 6 (January 1, 1995): 1276–85. https://doi.org/10.1007/BF02304886.
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    • Kiselev, A., and B. Simon. “Rank one perturbations with infinitesimal coupling.” Journal of Functional Analysis 130, no. 2 (January 1, 1995): 345–56. https://doi.org/10.1006/jfan.1995.1074.
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    • Choi, Kyudong, Thomas Y. Hou, Alexander Kiselev, Guo Luo, Vladimir Sverak, and Yao Yao. “On the Finite-Time Blowup of a 1D Model for the 3D Axisymmetric Euler Equations,” n.d.
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    • He, Siming, and Alexander Kiselev. “Small scale creation for solutions of the SQG equation,” n.d.
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    • Kiselev, Alexander, and Hang Yang. “Analysis of a Singular Boussinesq Model,” n.d.
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    • Kiselev, Alexander, and Lenya Ryzhik. “A simple model for asset price bubble formation and collapse,” n.d.

  • Conference Papers

    • Kiselev, Alexander. “Some recent results on the critical surface quasi-geostrophic equation: A review.” In Hyperbolic Problems: Theory, Numerics and Applications, Part 1, edited by E. Tadmor, J. Liu, and A. Tzavaras, 67:105–22. AMER MATHEMATICAL SOC, 2009.
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    • Kiselev, Alexander. “Diffusion and Mixing in Fluid Flow: A Review,” 357–69. Springer Netherlands, 2009. https://doi.org/10.1007/978-90-481-2810-5_24.
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• Teaching & Mentoring
• 

  Recent Courses

  • MATH 431: Advanced Calculus I 2019
  • MATH 631: Measure and Integration 2019
  • MATH 731: Advanced Calculus I 2019
  • MATH 557: Introduction to Partial Differential Equations 2018
  • MATH 690-32: Topics in Analysis 2018
  • MATH 212: Multivariable Calculus 2017
• 

  Advising & Mentoring

  • I am currently advising two graduate students (Hang Yang and Yishu Gong) and one postdoctoral fellow (Siming He). One of my graduate students, Chao Li, got his PhD this year (from Rice) and moved on to a position at Goldman Sachs. A postdoctoral fellow I mentored, Changhui Tan, moved on to a tenure track position at University of South Carolina this year. 
    
    I also serve as an advisor to two undergraduate students,  Amy Fan and Adam York, and I serve this year as a teaching mentor to postdoctoral fellow Nan Wu.
    
    
    
    
• Scholarly, Clinical, & Service Activities
• 

  Presentations & Appearances

  • Small scale creation in fluids. Analysis seminar. Kent University. November 2018  2018
  • Small scale creation in fluids. Colloquium. University of Toronto. November 2018  2018
  • Small scale creation in fluids. 82nd Midwest PDE seminar. October 2018  2018
  • Enhancement of reactions by chemotaxis. Banff International Research Station. August 2018  2018
  • Intorduction to Fluids. Summer Workshop in Math (SWiM). Duke University. June 2018  2018
  • Small scale creation in fluids. Workshop on Mathematical fine structures in fluid dynamics. Gran Sasso Science Institute, l'Aquila, Italy. June 2018 - June 2018  2018
  • Growth in solutions of 2D Euler equation. Colloquium. UCSD. April 2018  2018
  • Small Scale and Singularity Formation in Fluid Mechanics . SIAM conference on Partial Differential Equations. December 2017  2017
  • Suppression of chemotactic explosion by fluid flow . SIAM conference on Partial Differential Equations. December 2017  2017
  • Regularity Properties of Euler Alignment System. Reaction-Diffusion, Propagation, and Modelling. Institut Henri Poincare. November 2017  2017
  • Small scale creation in solutions of the 2D Euler equation . Analysis seminar. UNC Chapel Hill . October 2017  2017
  • Regularity and Blow Up for Active Scalars. Analysis seminar. Princeton University. September 2017  2017
  • Small scale creation in solutions of the 2D Euler equation . PDE seminar. Georgia Tech . September 2017  2017
  • Singularity Formation in Models of Fluid Mechanics. Summer school: Various Aspects of Mathematical Physics. Euler Institute . July 2017  2017
  • Singularity formation in modified SQG patches. Workshop Irregular transport: analysis and applications. University of Basel. July 2017  2017
  • Regularity and Blow Up for Active Scalars. Summer School and Workshop: Mathematical Analysis of Water Waves and Related Models. UC Davis. June 2017  2017
  • Enhancement of Biological Reactions by Chemotaxis . Colloquium. University of Miami. April 2017  2017
  • Small scale creation in solutions of the 2D Euler equation . Colloquium. USC. March 2017  2017
• 

  Service to the Profession

  • Coordinating Editor. Memoirs of the AMS. January 2019  2019
  • Coordinating Editor. Transactions of the AMS. January 2019  2019
  • Associate Editor, Dynamics of PDE. September 2017  2017
  • Editorial Board, Nonlinearity. January 2017  2017
  • Editorial Board, Memoirs of the AMS. January 2013  2013
  • Editorial Board, Transactions of the AMS. January 2013  2013
  • Associate Editor, Communications in Mathematical Sciences. January 2011  2011
• 

  Service to Duke

  • Appointments. 2018 - 2019  2018 - 2019
  • Appointments. 2017 - 2018  2017 - 2018
  • Postdoctoral Appointments. 2017 - 2018  2017 - 2018

Some information on this profile has been compiled automatically from Duke databases and external sources. (Our About page explains how this works.) If you see a problem with the information, please write to Scholars@Duke and let us know. We will reply promptly.