Alexander A. Kiselev
William T. Laprade Distinguished Professor of Mathematics
My current research interests focus on mathematical fluid mechanics and mathematical biology.
In the past, I have also worked on reaction-diffusion equations and spectral theory of Schredinger operators.
In the past, I have also worked on reaction-diffusion equations and spectral theory of Schredinger operators.
Current Research Interests
Mathematical Fluid Mechanics, Mathematical Biology, Reaction-Diffusion equations, Spectral theory of Schredinger operators
Current Appointments & Affiliations
- William T. Laprade Distinguished Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2018
- Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2017
Contact Information
- Background
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Education, Training, & Certifications
- Ph.D., California Institute of Technology 1997
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Leadership & Clinical Positions at Duke
- Managing Editor of Duke Mathematical Journal, 2022 - current
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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
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In the News
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JAN 13, 2020 Quanta Magazine -
OCT 5, 2017
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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
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Subject Headings
- Research
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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
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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
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External Relationships
- National University of Singapore
- Seoul National University
- University of Texas at Austin
- Publications & Artistic Works
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Selected Publications
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Academic Articles
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text Open Access Copy
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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.Full Text
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Kiselev, Alexander, and Xiaoyutao Luo. “On nonexistence of splash singularities for the $α$-SQG patches,” November 26, 2021.Link to Item
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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.Full Text
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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
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Gong, Yishu, and Alexander Kiselev. “Chemotactic Reaction Enhancement in One Dimension,” March 26, 2021.Link to Item
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Kiselev, Alexander, and Yao Yao. “Small scale formations in the incompressible porous media equation,” February 9, 2021.Link to Item
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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.Full Text
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Kiselev, Alexander, and Changhui Tan. “The Flow of Polynomial Roots Under Differentiation,” December 16, 2020.Link to Item
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Kiselev, Alexander, Fedor Nazarov, Lenya Ryzhik, and Yao Yao. “Chemotaxis and Reactions in Biology,” April 14, 2020.Link to Item
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text Open Access Copy
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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.Full Text
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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.Full Text Open Access Copy
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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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.Full Text
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Kiselev, Alexander, and Hang Yang. “Analysis of a Singular Boussinesq Model.” Research in the Mathematical Sciences 6 (n.d.).Link to Item
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Kiselev, Alexander, and Lenya Ryzhik. “A simple model for asset price bubble formation and collapse,” n.d.
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Book Sections
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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.Full Text
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Digital Publications
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He, Siming, and Alexander Kiselev. “Stirring Speeds Up Chemical Reaction.” arxiv.org, n.d.Link to Item
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Conference Papers
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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.Full Text Link to Item
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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.Link to Item
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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.Full Text
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Preprints
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Hu, Zhongtian, Alexander Kiselev, and Yao Yao. “Suppression of chemotactic singularity by buoyancy,” May 1, 2023.Link to Item
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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.Link to Item
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Kiselev, Alexander, Jaemin Park, and Yao Yao. “Small scale formation for the 2D Boussinesq equation,” November 9, 2022.Link to Item
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Kiselev, Alexander, and Xiaoyutao Luo. “Illposedness of $C^{2}$ vortex patches,” April 13, 2022.Link to Item
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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.Link to Item
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- Teaching & Mentoring
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Recent Courses
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Advising & Mentoring
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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
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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.
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Co-organizer (with Tarek Elgindi and Jim Nolen) of the 2022 RTG summer school for graduate students and postdocs at Duke.
- Scholarly, Clinical, & Service Activities
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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
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Outreach & Engaged Scholarship
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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
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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
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Academic & Administrative Activities
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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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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.
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.