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)

Christ, M., and A. Kiselev. “WKB and spectral analysis of one-dimensional Schrödinger operators with slowly varying potentials.” Communications in Mathematical Physics, vol. 218, no. 2, Jan. 2001, pp. 245–62. Scopus, doi:10.1007/PL00005556. Full Text

Kiselev, A. “Absolutely continuous spectrum of perturbed stark operators.” Transactions of the American Mathematical Society, vol. 352, no. 1, Dec. 2000, pp. 243–56.

Kiselev, A., and Y. Last. “Solutions, spectrum, and dynamics for schrödinger operators on infinite domains.” Duke Mathematical Journal, vol. 102, no. 1, Jan. 2000, pp. 125–50. Scopus, doi:10.1215/S0012-7094-00-10215-3. Full Text

Constantin, P., et al. “Bulk burning rate in passive-reactive diffusion.” Archive for Rational Mechanics and Analysis, vol. 154, no. 1, Jan. 2000, pp. 53–91. Scopus, doi:10.1007/s002050000090. Full Text

Kiselev, A. “An interpolation theorem related to the A.E. convergence of integral operators.” Proceedings of the American Mathematical Society, vol. 127, no. 6, Dec. 1999, pp. 1781–85.

Kiselev, A., et al. “Effective perturbation methods for one-dimensional Schrödinger operators.” Journal of Differential Equations, vol. 151, no. 2, Jan. 1999, pp. 290–312. Scopus, doi:10.1006/jdeq.1998.3514. Full Text

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, vol. 11, no. 4, Oct. 1998, pp. 771–97.

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, vol. 94, no. 3, Jan. 1998, pp. 619–46. Scopus, doi:10.1215/S0012-7094-98-09425-X. Full Text

Kiselev, A., et al. “Modified prüfer and EFGP transforms and the spectral analysis of one dimensional schrödinger operators.” Communications in Mathematical Physics, vol. 194, no. 1, Jan. 1998. Scopus, doi:10.1007/s002200050346. Full Text

Kiselev, A. “Some examples in one-dimensional "geometric" scattering on manifolds.” Journal of Mathematical Analysis and Applications, vol. 212, no. 1, Aug. 1997, pp. 263–80. Scopus, doi:10.1006/jmaa.1997.5497. Full Text

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