Scholars@Duke

• Background
• 

  Education, Training, & Certifications

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

  Leadership & Clinical Positions at Duke

  • Managing Editor of Duke Mathematical Journal, 2022 - current 
• 

  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

  • JAN 13, 2020

    Quanta Magazine

    For fluid equations, a steady flow of progress

  • OCT 5, 2017

    Alexander Kiselev: Mixing It Up
• 

  Awards & Honors

  • Simons Fellowship. Simons Foundation. 2020
  • 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

  • Small Scale and Singularity Formation in Fluids awarded by  National Science Foundation 2023 - 2026
  • RTG: Training Tomorrow's Workforce in Analysis and Applications awarded by  National Science Foundation 2021 - 2026
  • Small Scale and Singularity Formation in Fluids awarded by  National Science Foundation 2020 - 2023
  • Small Scale and Singularity Formation in Fluid Mechanics and Biology awarded by Simons Foundation 2020 - 2022
  • Regularity, blow up and mixing in fluids awarded by  National Science Foundation 2018 - 2022
• 

  Fellowships, Supported Research, & Other Grants

  • Training Tomorrow's Workforce awarded by NSF 2021 - 2026
  • Simons Fellowship awarded by Simons Foundation 2020 - 2022
  • Small scale and singularity formation in fluids awarded by NSF 2020 - 2023
  • Regularity, Blow UP, and Mixing in Fluids awarded by NSF 2017 - 2020
  • Topics in Applied PDE awarded by NSF 2014 - 2018
• 

  External Relationships

  • National University of Singapore
  • Seoul National University
  • University of Texas at Austin
• Publications & Artistic Works
• 

  Selected Publications

  • Academic Articles

    • Kiselev, A., and Y. Yao. “Small Scale Formations in the Incompressible Porous Media Equation.” Archive for Rational Mechanics and Analysis 247, no. 1 (February 1, 2023). https://doi.org/10.1007/s00205-022-01830-z.
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    • Kiselev, A., and C. Tan. “The Flow of Polynomial Roots Under Differentiation.” Annals of Pde 8, no. 2 (December 1, 2022). https://doi.org/10.1007/s40818-022-00135-4.
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    • Gong, Yishu, Siming He, and Alexander Kiselev. “Random Search in Fluid Flow Aided by Chemotaxis.” Bulletin of Mathematical Biology 84, no. 7 (June 2022): 71. https://doi.org/10.1007/s11538-022-01024-4.
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    • Chouliara, D., Y. Gong, S. He, A. Kiselev, J. Lim, O. Melikechi, and K. Powers. “Hitting time of Brownian motion subject to shear flow.” Involve 15, no. 1 (January 1, 2022): 131–40. https://doi.org/10.2140/involve.2022.15.131.
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    • Kiselev, A., and C. Tan. “GLOBAL REGULARITY FOR A NONLOCAL PDE DESCRIBING EVOLUTION OF POLYNOMIAL ROOTS UNDER DIFFERENTIATION.” Siam Journal on Mathematical Analysis 54, no. 3 (January 1, 2022): 3161–91. https://doi.org/10.1137/21M1422859.
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    • Kiselev, Alexander, and Xiaoyutao Luo. “On nonexistence of splash singularities for the $α$-SQG patches,” November 26, 2021.
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    • He, S., and A. Kiselev. “Boundary layer models of the Hou-Luo scenario.” Journal of Differential Equations 298 (October 15, 2021): 182–204. https://doi.org/10.1016/j.jde.2021.07.007.
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    • Gong, Yishu, Siming He, and Alexander Kiselev. “Random search in fluid flow aided by chemotaxis,” July 6, 2021.
       Open Access Copy  Link to Item
    • Gong, Yishu, and Alexander Kiselev. “Chemotactic Reaction Enhancement in One Dimension,” March 26, 2021.
       Link to Item
    • Kiselev, Alexander, and Yao Yao. “Small scale formations in the incompressible porous media equation,” February 9, 2021.
       Link to Item
    • He, S., and A. Kiselev. “Small-scale creation for solutions of the sqg equation.” Duke Mathematical Journal 170, no. 5 (January 1, 2021): 1027–41. https://doi.org/10.1215/00127094-2020-0064.
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    • Kiselev, Alexander, and Changhui Tan. “The Flow of Polynomial Roots Under Differentiation,” December 16, 2020.
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    • Kiselev, Alexander, Fedor Nazarov, Lenya Ryzhik, and Yao Yao. “Chemotaxis and Reactions in Biology,” April 14, 2020.
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    • 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): 1–37. 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 (October 5, 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 (March 1, 2015): 1667–79. https://doi.org/10.1007/s00220-014-2146-2.
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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,” July 17, 2014.
       Link to Item
    • 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 (January 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.
       Link to Item
    • 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. https://doi.org/10.1155/imrn.2005.2315.
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    • Kiselev, A. “Imbedded singular continuous spectrum for Schrödinger operators.” Journal of the American Mathematical Society 18, no. 3 (July 1, 2005): 571–603. https://doi.org/10.1090/S0894-0347-05-00489-3.
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    • 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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    • 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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    • Killip, R., A. Kiselev, and Y. Last. “Dynamical upper bounds on wavepacket spreading.” American Journal of Mathematics 125, no. 5 (January 1, 2003): 1165–98. https://doi.org/10.1353/ajm.2003.0031.
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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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    • 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. “Absolutely continuous spectrum of perturbed stark operators.” Transactions of the American Mathematical Society 352, no. 1 (January 1, 2000): 243–56. https://doi.org/10.1090/s0002-9947-99-02450-2.
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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., 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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    • Kiselev, A. “An interpolation theorem related to the A.E. convergence of integral operators.” Proceedings of the American Mathematical Society 127, no. 6 (January 1, 1999): 1781–85. https://doi.org/10.1090/s0002-9939-99-04681-x.
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    • Christ, M., and A. Kiselev. “Absolutely continuous spectrum for one-dimensional Schrödinger operators with slowly decaying potentials: Some optimal results.” Journal of the American Mathematical Society 11, no. 4 (January 1, 1998): 771–97. https://doi.org/10.1090/s0894-0347-98-00276-8.
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    • 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): 1–45. 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 (January 1, 1996): 377–99. https://doi.org/10.1007/bf02102594.
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    • 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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    • Kiselev, A. A., and B. S. Pavlov. “Eigenfrequencies and eigenfunctions of the Laplacian for Neumann boundary conditions in a system of two coupled cavities.” Theoretical and Mathematical Physics 100, no. 3 (September 1, 1994): 1065–74. https://doi.org/10.1007/BF01018571.
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    • Kiselev, A. A., and B. S. Pavlov. “Essential spectrum of the Laplacian for the Neumann problem in a model region of complicated structure.” Theoretical and Mathematical Physics 99, no. 1 (April 1, 1994): 383–95. https://doi.org/10.1007/BF01018792.
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    • Kiselev, Alexander, and Hang Yang. “Analysis of a Singular Boussinesq Model.” Research in the Mathematical Sciences 6 (n.d.).
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    • Kiselev, Alexander, and Lenya Ryzhik. “A simple model for asset price bubble formation and collapse,” n.d.

  • Book Sections

    • Kiselev, A. A. “Small Scale Creation in Active Scalars.” In Lecture Notes in Mathematics, 2272:125–61, 2020. https://doi.org/10.1007/978-3-030-54899-5_4.
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  • Digital Publications

    • He, Siming, and Alexander Kiselev. “Stirring Speeds Up Chemical Reaction.” arxiv.org, n.d.
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  • Conference Papers

    • Kiselev, Alexander A. “Small Scale Creation in Active Scalars.” In Progress in Mathematical Fluid Dynamics, 2272:123–59, 2020. https://doi.org/10.1007/978-3-030-54899-5_4.
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    • 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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  • Preprints

    • Hu, Zhongtian, Alexander Kiselev, and Yao Yao. “Suppression of chemotactic singularity by buoyancy,” May 1, 2023.
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    • Gong, Yishu, and Alexander Kiselev. “A simple reaction-diffusion system as a model for the origin of chemotaxis,” November 13, 2022.
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    • Kiselev, Alexander, Jaemin Park, and Yao Yao. “Small scale formation for the 2D Boussinesq equation,” November 9, 2022.
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    • Kiselev, Alexander, and Xiaoyutao Luo. “Illposedness of $C^{2}$ vortex patches,” April 13, 2022.
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    • Kiselev, Alexander. “Preservation of the absolutely continuous spectrum of Schrödinger equation under perturbations by slowly decreasing potentials and a.e. convergence of integral operators,” September 30, 1996.
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• Teaching & Mentoring
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  Recent Courses

  • MATH 790-90: Minicourse in Advanced Topics 2023
  • MATH 431: Introduction to Real Analysis 2022
  • MATH 731: Introduction to Real Analysis 2022
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  Advising & Mentoring

  • 
    Graduate Students and postdocs: 
    
    Zhongtian (Kevin) Hu, 2020 - current, graduate student
    
    Kevin Dembski, 2021 - 2022, graduate student, first year mentor
    
    Logan Stokols, 2021 - current, postdoctoral fellow
    
    Xiaoyutao Luo, 2020 - current, postdoctoral fellow
    
    Siming He, 2019 - 2022, postdoctoral fellow, moved on as tenure-track assistant professor at University of South Carolina
    
    Yishu Gong, 2017 - 2022, PhD 2022, graduate student, moved on as a research at Takeda corporation, Boston
    
    Undergraduate students: 
    
    Sara Azimi, Daniel Bliss, Rachel Odonkor, and Marie-Helene Thome, research project in 2022 
    
    Despina Chouliara, James Lim and Keenan Powers, DoMath research project in 2022
    
    Vincent Li, Zachary McCarthy, Gregory Orme, and Santino Panzica - current advisees
    
     
    
    
    
    
    
    
    
    
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  Teaching Activities

  • Co-organizer (with Tarek Elgindi and Jim Nolen) of the 2022 RTG summer school for graduate students and postdocs at Duke. 
    
    Sponsor of the semester REU activity in Spring 2022. 
    
    Co-organizer (with Tarek Elgindi) of the RTG working seminar in Fall 2021 (on fluid mechanics).
    
    Sponsor of the DoMath undergraduate research summer project, 2020. 
    
    
    
• Scholarly, Clinical, & Service Activities
• 

  Presentations & Appearances

  • Regularity of vortex and SQG patch evolution. MathFlows Conference. CIRM. December 2022  2022
  • The flow of polynomial roots under differentiation. PDE and Geometric Analysis seminar. UW-Madison. October 2022  2022
  • "Singularities in differential equations". Undergraduate Symposium. Duke University. September 2022  2022
  • Two stories in PDE. Summer School on Partial Differential Equations. University of Texas. August 2022  2022
  • On regularity and ill-posedness of patch evolution . AIM Square "Towards a 3D Euler singularity". AIM Institute. July 2022  2022
  • Regularity of vortex and SQG patches. Workshop ``Small scale dynamics in fluid motion". Simons Center, Stony Brook University. June 2022  2022
  • The flow of polynomial roots under differentiation. SIAM webinar in the Analysis and Methods of PDE. SIAM. June 2022  2022
  • Ill-posedness of vortex and SQG patches. Workshop "Criticality and stochasticity in quasilinear fluid systems". AIM Institute. May 2022  2022
  • Small scale creation in active scalars. Workshop . Newton Institute. February 2022  2022
  • The flow of polynomial roots under differentiation. PDE and Analysis seminar. UNC Chapel Hill. February 2022  2022
  • Small scale formation in solutions of active scalar equations. Nonlinear Analysis Seminar. Rutgers University. December 2021  2021
  • Chemotaxis and Reactions in Biology. Virtual Analysis and PDE. UC Irvine and UC San Diego. November 2021  2021
  • Small scales and singularity formation in fluid mechanics. Moscow Paris Seminar Dynamical Systems and PDE. November 2021  2021
  • The flow of polynomial roots under differentiation. Colloquium . Stony Brook University. November 2021  2021
  • Singularity formation in a boundary layer model of the Hou-Luo scenario. Singularity Formation in Nonlinear PDE. Banff International Research Station. September 2021  2021
  • The flow of polynomial roots under differentiation. Mathematical Challenge of Quantum Transport in Nanosystems. ITMO, St. Peterburg. September 2021  2021
  • The flow of polynomial roots under differentiation. One World PDE seminar. University of Bath. April 2021  2021
  • The flow of polynomial roots under differentiation. Seminar on Fluids. MSRI. March 2021  2021
  • The flow of polynomial roots under differentiation. Applied Mathematics Seminar. Stanford University. February 2021  2021
  • The flow of polynomial roots under differentiation. Long time behavior and singularity formation in PDE. Institute for Turbulence Research. January 2021  2021
  • Small scales and singularity formation in fluid mechanics. Colloquium . University of Minnesota . November 2020  2020
  • Small scale formation in solutions of active scalar equations. Applied Mathematics seminar. USC. October 2020  2020
  • Small scales formation in fluids. Industrial Mathematics Seminar. St Petersburg State University. October 2020  2020
  • Small scales and singularity formation in fluid mechanics. Harbin Institute of Technology summer school. Harbin Institute of Technology. July 2020  2020
  • Small scale creation in fluid mechanics. Virginia Tech . December 2019  2019
  • Chemotaxis and reactions in biology . KI-Net "Research on weekend". University of Maryland. September 2019  2019
  • Small scale creation for the SQG equation. Formation of small scales in nonlinear PDEs. University of Maryland. September 2019  2019
  • Growth of derivatives in solutions of the SQG equation. AIM Square meeting on 3D Euler equation. American Institute of Mathematics. August 2019  2019
  • Regularity and blow up in active scalars. Summer School on Fluid Dynamics, six hour course. CIME. June 2019  2019
  • Small scales in solutions of the 2D Euler equation. NC State University . April 2019  2019
  • Singularity and small scale formation in fluids. University of Pittsburgh. March 2019  2019
  • Small scale creation in fluid mechanics. Workshop Essence of (u \cdot \nabla) u: Reflections on Mathematical Fluid Dynamics. University of Virginia. March 2019  2019
  • Understanding the Hou-Luo singular scenario. Workshop on Fluid turbulence and Singularities of the Euler/Navier Stokes equations. Harvard University. March 2019  2019
  • On 1D models of Hou-Luo scenario. Brown University. February 2019  2019
  • Small scale creation in fluid mechanics. University of South Carolina. February 2019  2019
  • Small scale creation in fluid mechanics. 12th Brooke Benjamin Lecture . University of Oxford. January 2019  2019
  • 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
• 

  Outreach & Engaged Scholarship

  • Co-organizer. Undergraduate Research Symposium. Duke University. October 2021  2021
  • Supervisor. DoMath project. June 2020 - July 2020  2020
• 

  Service to the Profession

  • Managing Editor. Duke Mathematical Journal. January 2022  2022
  • NSF grant panel. October 2021  2021
  • Coordinating Editor. Memoirs of the AMS. February 2019 - February 2021  2019 - 2021
  • Coordinating Editor. Transactions of the AMS. February 2019 - February 2021  2019 - 2021
  • Associate Editor, Dynamics of PDE. September 2017  2017
  • Editorial Board, Nonlinearity. January 2017 - December 2021  2017 - 2021
  • Editorial Board, Transactions of the AMS. February 2013 - February 2021  2013 - 2021
  • Editorial Board, Memoirs of the AMS. January 2013 - February 2021  2013 - 2021
  • Associate Editor, Communications in Mathematical Sciences. January 2011  2011
• 

  Service to Duke

  • Tenure-track hiring committee. November 2021  2021
  • Promotion to Professor, Chair. 2020  2020
  • Promotion to tenure. 2020  2020
  • Chair of a Committee. September 2019  2019
  • Appointments. 2018 - 2019  2018 - 2019
  • Appointments. 2017 - 2018  2017 - 2018
  • Postdoctoral Appointments. 2017 - 2018  2017 - 2018
• 

  Academic & Administrative Activities

  • I serve as the PI on the NSF-RTG grant involving multiple personnel across different levels, and as the PI on an  individual NSF grants.
    
    I currently advise or co-advise four postdoctoral fellows, two graduate students, and three undergraduates. 
    
    I am in the process of organizing the semester REU program for several undergraduate students that is a part of the RTG project that will run in Spring 2022, and a summer RTG school for graduate students and postdocs that will run in August 2022. 
    
    
    

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