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

  • 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

  • Conference Papers

    • Kiselev, A. "Some recent results on the critical surface quasi-geostrophic equation: A review." 2009.  Link to Item
    • Kiselev, A. "Diffusion and Mixing in Fluid Flow: A Review." 2009.  Full Text  Link to Item

  • Journal Articles

    • Do, T, Kiselev, A, Ryzhik, L, and Tan, C. "Global Regularity for the Fractional Euler Alignment System." Archive for Rational Mechanics and Analysis 228, no. 1 (April 2018): 1-37.  Full Text  Open Access Copy
    • Kiselev, A, and Tan, C. "Finite time blow up in the hyperbolic Boussinesq system." Advances in Mathematics 325 (February 2018): 34-55.  Full Text
    • Choi, K, Hou, TY, Kiselev, A, Luo, G, Sverak, V, and Yao, Y. "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 2017): 2218-2243.  Full Text
    • Kiselev, A, Yao, Y, and Zlatoš, A. "Local Regularity for the Modified SQG Patch Equation." Communications on Pure and Applied Mathematics 70, no. 7 (July 2017): 1253-1315.  Full Text
    • Kiselev, A, Ryzhik, L, Yao, Y, and Zlatoš, A. "Finite time singularity for the modified SQG patch equation." Annals of Mathematics 184, no. 3 (November 1, 2016): 909-948.  Full Text
    • Kiselev, A, and Xu, X. "Suppression of Chemotactic Explosion by Mixing." Archive for Rational Mechanics and Analysis 222, no. 2 (November 2016): 1077-1112.  Full Text
    • Popov, I, Kurasov, P, Naboko, S, Kiselev, A, Ryzhkov, A, Yafyasov, A, Miroshnichenko, G, Karpeshina, Y, Kruglov, V, Pankratova, T, and Popov, A. "A distinguished mathematical physicist Boris S. Pavlov." Nanosystems: Physics, Chemistry, Mathematics (October 25, 2016): 782-788.  Full Text
    • Kiselev, A, and Zlatoš, A. "Blow up for the 2D Euler equation on some bounded domains." Journal of Differential Equations 259, no. 7 (October 2015): 3490-3494.  Full Text
    • Choi, K, Kiselev, A, and Yao, Y. "Finite Time Blow Up for a 1D Model of 2D Boussinesq System." Communications in Mathematical Physics 334, no. 3 (March 2015): 1667-1679.  Full Text
    • Kiselev, A, and Šverák, V. "Small scale creation for solutions of the incompressible two-dimensional Euler equation." Annals of Mathematics (November 1, 2014): 1205-1220.  Full Text
    • Iyer, G, Kiselev, A, and Xu, X. "Lower bounds on the mix norm of passive scalars advected by incompressible enstrophy-constrained flows." Nonlinearity 27, no. 5 (May 1, 2014): 973-985.  Full Text
    • Dabkowski, M, Kiselev, A, Silvestre, L, and Vicol, V. "Global well-posedness of slightly supercritical active scalar equations." Analysis & PDE 7, no. 1 (2014): 43-72.  Full Text
    • Kiselev, A, and Nazarov, F. "A simple energy pump for the surface quasi-geostrophic equation." Nonlinear Partial Differential Equations: The Abel Symposium 2010 (December 1, 2012): 175-179.  Full Text
    • Kiselev, A, and Ryzhik, L. "Biomixing by chemotaxis and efficiency of biological reactions: The critical reaction case." Journal of Mathematical Physics 53, no. 11 (November 2012): 115609-115609.  Full Text
    • Dabkowski, M, Kiselev, A, and Vicol, V. "Global well-posedness for a slightly supercritical surface quasi-geostrophic equation." Nonlinearity 25, no. 5 (May 1, 2012): 1525-1535.  Full Text
    • Kiselev, A, and Ryzhik, L. "Biomixing by Chemotaxis and Enhancement of Biological Reactions." Communications in Partial Differential Equations 37, no. 2 (February 2012): 298-318.  Full Text
    • Kiselev, A. "Nonlocal maximum principles for active scalars." Advances in Mathematics 227, no. 5 (August 2011): 1806-1826.  Full Text
    • Kiselev, A, and Nazarov, F. "Variation on a theme of caffarelli and vasseur." Journal of Mathematical Sciences 166, no. 1 (April 2010): 31-39.  Full Text
    • Kiselev, A, and Nazarov, F. "Global regularity for the critical dispersive dissipative surface quasi-geostrophic equation." Nonlinearity 23, no. 3 (March 1, 2010): 549-554.  Full Text
    • Berestycki, H, Kiselev, A, Novikov, A, and Ryzhik, L. "The explosion problem in a flow." Journal d'Analyse Mathématique 110, no. 1 (January 2010): 31-65.  Full Text
    • Kiselev, A. "Regularity and Blow up for Active Scalars." Mathematical Modelling of Natural Phenomena 5, no. 4 (2010): 225-255.  Full Text
    • Kim, A, and Kiselev, A. "Absolutely continuous spectrum of discrete Schrödinger operators with slowly oscillating potentials." Mathematische Nachrichten 282, no. 4 (April 2009): 552-568.  Full Text
    • Constantin, P, Kiselev, A, Ryzhik, L, and Zlatoš, A. "Diffusion and mixing in fluid flow." Annals of Mathematics 168, no. 2 (September 1, 2008): 643-674.  Full Text
    • Kiselev, A, Nazarov, F, and Shterenberg, R. "Blow up and regularity for fractal Burgers equation." Dynamics of Partial Differential Equations 5, no. 3 (2008): 211-240.  Full Text
    • Kiselev, A, Shterenberg, R, and Zlatos, A. "Relaxation enhancement by time-periodic flows." Indiana University Mathematics Journal 57, no. 5 (2008): 2137-2152.  Full Text
    • Kiselev, A, Nazarov, F, and Volberg, A. "Global well-posedness for the critical 2D dissipative quasi-geostrophic equation." Inventiones Mathematicae 167, no. 3 (January 27, 2007): 445-453.  Full Text
    • Denisov, SA, and Kiselev, A. "Spectral properties of schrodinger operators with decaying potentials." Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday 76 (2007): 565-589.  Link to Item
    • Kiselev, A, and Zlatoš, A. "Quenching of combustion by shear flows." Duke Mathematical Journal 132, no. 1 (March 2006): 49-72.  Full Text
    • Fannjiang, A, Kiselev, A, and Ryzhik, L. "Quenching of reaction by cellular flows." GAFA Geometric And Functional Analysis 16, no. 1 (February 2006): 40-69.  Full Text
    • Andrzejewski, D, Butzlaff, E, Kiselev, A, and Markely, LRA. "Enhancement of combustion by drift in a coupled reaction-diffusion model." Communications in Mathematical Sciences 4, no. 1 (2006): 213-225.  Full Text
    • Berestycki, H, Hamel, F, Kiselev, A, and Ryzhik, L. "Quenching and Propagation in KPP Reaction-Diffusion Equations with a Heat Loss." Archive for Rational Mechanics and Analysis 178, no. 1 (October 2005): 57-80.  Full Text
    • Kiselev, A, and Zlatoš, A. "On discrete models of the Euler equation." International Mathematics Research Notices , no. 38 (August 28, 2005): 2315-2339. (Review)
    • 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, F, Kiselev, A, and Tcheremchantsev, S. "Transfer matrices and transport for Schrödinger operators." Annales de l’institut Fourier 54, no. 3 (2004): 787-830.  Full Text
    • Constantin, P, Kiselev, A, and Ryzhik, L. "Fronts in reactive convection: Bounds, stability, and instability." Communications on Pure and Applied Mathematics 56, no. 12 (December 2003): 1781-1803.  Full Text
    • Vladimirova, N, Constantin, P, Kiselev, A, Ruchayskiy, O, and Ryzhik, L. "Flame enhancement and quenching in fluid flows." Combustion Theory and Modelling 7, no. 3 (September 2003): 487-508.  Full Text
    • Christ, M, and Kiselev, A. "Absolutely continuous spectrum of Stark operators." Arkiv för Matematik 41, no. 1 (April 2003): 1-33.  Full Text
    • Kiselev, A, Last, Y, and Simon, B. "Stability of singular spectral types under decaying perturbations." Journal of Functional Analysis 198, no. 1 (February 2003): 1-27.  Full Text
    • Killip, R, Kiselev, A, and Last, Y. "Dynamical upper bounds on wavepacket spreading." American Journal of Mathematics 125, no. 5 (2003): 1165-1198.  Full Text
    • Christ, M, and Kiselev, A. "Scattering and Wave Operators for One-Dimensional Schr�dinger Operators with Slowly Decaying Nonsmooth Potentials." Geometrical and Functional Analysis Gafa 12, no. 6 (December 2002): 1174-1234.  Full Text
    • Gesztesy, F, Kiselev, A, and Makarov, KA. "Uniqueness Results for Matrix-Valued Schrödinger, Jacobi, and Dirac-Type Operators." Mathematische Nachrichten 239-240, no. 1 (June 2002): 103-145.  Full Text
    • Constantin, P, Kiselev, A, and Ryzhik, L. "Quenching of flames by fluid advection." Communications on Pure and Applied Mathematics 54, no. 11 (November 2001): 1320-1342.  Full Text
    • Kiselev, A, and Ryzhik, L. "An upper bound for the bulk burning rate for systems." Nonlinearity 14, no. 5 (September 1, 2001): 1297-1310.  Full Text
    • Kiselev, A, and Ryzhik, L. "Enhancement of the traveling front speeds in reaction-diffusion equations with advection." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 18, no. 3 (May 2001): 309-358.  Full Text
    • Christ, M, and Kiselev, A. "WKB and Spectral Analysis¶of One-Dimensional Schrödinger Operators¶with Slowly Varying Potentials." Communications in Mathematical Physics 218, no. 2 (April 2001): 245-262.  Full Text
    • Christ, M, and Kiselev, A. "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 2001): 426-447.  Full Text
    • Christ, M, and Kiselev, A. "Maximal Functions Associated to Filtrations." Journal of Functional Analysis 179, no. 2 (February 2001): 409-425.  Full Text
    • 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, Kiselev, A, Oberman, A, and Ryzhik, L. "Bulk Burning Rate in¶Passive–Reactive Diffusion." Archive for Rational Mechanics and Analysis 154, no. 1 (August 2000): 53-91.  Full Text
    • Last, Y, and Kiselev, A. "Solutions, spectrum, and dynamics for Schr�dinger operators on infinite domains." Duke Mathematical Journal 102, no. 1 (March 2000): 125-150.  Full Text
    • 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, Remling, C, and Simon, B. "Effective Perturbation Methods for One-Dimensional Schrödinger Operators." Journal of Differential Equations 151, no. 2 (January 1999): 290-312.  Full Text
    • 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. "and a.e. convergence of integral operators." Duke Mathematical Journal 94, no. 3 (September 1998): 619-646.  Full Text
    • Kiselev, A, Last, Y, and Simon, B. "Modified Prüfer and EFGP Transforms and the Spectral Analysis of One-Dimensional Schrödinger Operators." Communications in Mathematical Physics 194, no. 1 (May 1, 1998): 1-45.  Full Text
    • Kiselev, A. "Some Examples in One-Dimensional “Geometric” Scattering on Manifolds." Journal of Mathematical Analysis and Applications 212, no. 1 (August 1997): 263-280.  Full Text
    • Christ, M, Kiselev, A, and Remling, C. "The absolutely continuous spectrum of one-dimensional Schrödinger operators with decaying potentials." Mathematical Research Letters 4, no. 5 (1997): 719-723.  Full Text
    • Kiselev, A. "Absolutely continuous spectrum of one-dimensional Schrödinger operators and Jacobi matrices with slowly decreasing potentials." Communications in Mathematical Physics 179, no. 2 (August 1996): 377-399.  Full Text
    • Kiselev, AA, and Popov, IY. "Indefinite metric and scattering by a domain with a small hole." Mathematical Notes 58, no. 6 (December 1995): 1276-1285.  Full Text
    • Kiselev, A, and Simon, B. "Rank One Perturbations with Infinitesimal Coupling." Journal of Functional Analysis 130, no. 2 (June 1995): 345-356.  Full Text
    • Choi, K, Hou, TY, Kiselev, A, Luo, G, Sverak, V, and Yao, Y. "On the Finite-Time Blowup of a 1D Model for the 3D Axisymmetric Euler Equations."  Link to Item
    • Do, T, Kiselev, A, and Xu, X. "Stability of Blowup for a 1D Model of Axisymmetric 3D Euler Equation (Published online)." Journal of Nonlinear Science .  Full Text
    • Kiselev, A, and Li, C. "Global Regularity and Fast Small Scale Formation for Euler Patch Equation in a Smooth Domain." .  Link to Item
    • Kiselev, A, and Ryzhik, L. "A simple model for asset price bubble formation and collapse."
    • Kiselev, A, and Tan, C. "Global regularity for 1D Eulerian dynamics with singular interaction forces."  Open Access Copy  Link to Item
    • Kiselev, A, and Yang, H. "Analysis of a Singular Boussinesq Model." .  Link to Item
    • Kiselev, A. "Special Issue Editorial: Small Scales and Singularity Formation in Fluid Dynamics(Published online)." Journal of Nonlinear Science .  Full Text
• Teaching & Mentoring
• 

  Recent Courses

  • 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 three graduate students (Chao Li, Hang Yang and Yishu Gong) and one postdoctoral fellow (Changhui Tan). Yishu Gong is the second year student here at Duke; Hang Yang is visiting here at Duke from Rice. Chao Li is at Rice and expected to graduate in 2018, Changhui Tan finishes his term at Rice in 2018. 
• Scholarly, Clinical, & Service Activities
• 

  Presentations & Appearances

  • 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

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

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