Alexander A. Kiselev

Alexander A. Kiselev
  • William T. Laprade Distinguished Professor of Mathematics
  • Professor of Mathematics

Research Areas and Keywords

Analysis

Fourier analysis, functional analysis

Biological Modeling

Chemotaxis, enhancement of biological reactions

Mathematical Physics

Spectral theory, Schrodinger operators

PDE & Dynamical Systems

Fluid mechanics, Euler equation, surface quasi-geostrophic equation, singularity formation, small scale creation, mixing efficiency

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. 

Education & Training
  • Ph.D., California Institute of Technology 1997

Fellowships, Supported Research, & Other Grants

Regularity, Blow UP, and Mixing in Fluids awarded by NSF (2017 to 2020)

Topics in Applied PDE awarded by NSF (2014 to 2018)

Denisov, Sergey A., and Alexander Kiselev. “Spectral properties of schrodinger operators with decaying potentials.” Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon’S 60th Birthday, edited by F. Gesztesy et al., vol. 76, AMER MATHEMATICAL SOC, Jan. 2007, pp. 565–89.

Kiselev, A., and A. Zlatoš. “Quenching of combustion by shear flows.” Duke Mathematical Journal, vol. 132, no. 1, Mar. 2006, pp. 49–72. Scopus, doi:10.1215/S0012-7094-06-13212-X. Full Text

Fannjiang, A., et al. “Quenching of reaction by cellular flows.” Geometric and Functional Analysis, vol. 16, no. 1, Feb. 2006, pp. 40–69. Scopus, doi:10.1007/s00039-006-0554-y. Full Text

Andrzejewski, David, et al. “Enhancement of combustion by drift in a coupled reaction-diffusion model.” Communications in Mathematical Sciences, vol. 4, no. 1, International Press of Boston, 2006, pp. 213–25. Crossref, doi:10.4310/cms.2006.v4.n1.a8. Full Text

Berestycki, H., et al. “Quenching and propagation in KPP reaction-diffusion equations with a heat loss.” Archive for Rational Mechanics and Analysis, vol. 178, no. 1, Oct. 2005, pp. 57–80. Scopus, doi:10.1007/s00205-005-0367-4. Full Text

Kiselev, A., and A. Zlatoš. “On discrete models of the Euler equation.” International Mathematics Research Notices, no. 38, Aug. 2005, pp. 2315–39.

Kiselev, A. “Imbedded singular continuous spectrum for Schrödinger operators.” Journal of the American Mathematical Society, vol. 18, no. 3, July 2005, pp. 571–603. Scopus, doi:10.1090/S0894-0347-05-00489-3. Full Text

Germinet, François, et al. “Transfer matrices and transport for Schrödinger operators.” Annales De L’Institut Fourier, vol. 54, no. 3, Cellule MathDoc/CEDRAM, 2004, pp. 787–830. Crossref, doi:10.5802/aif.2034. Full Text

Constantin, P., et al. “Fronts in Reactive Convection: Bounds, Stability, and Instability.” Communications on Pure and Applied Mathematics, vol. 56, no. 12, Dec. 2003, pp. 1781–803. Scopus, doi:10.1002/cpa.10110. Full Text

Killip, R., et al. “Dynamical upper bounds on wavepacket spreading.” American Journal of Mathematics, vol. 125, no. 5, Oct. 2003, pp. 1165–98.

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