# Alexander A. Kiselev

- William T. Laprade Distinguished Professor of Mathematics
- Professor of Mathematics

##### Links

### 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.

### 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., et al. “The absolutely continuous spectrum of one-dimensional Schrödinger operators with decaying potentials.” *Mathematical Research Letters*, vol. 4, no. 5, Jan. 1997, pp. 719–23. *Scopus*, doi: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*, vol. 179, no. 2, Jan. 1996, pp. 377–99.

Kiselev, A. A., and I. Y. Popov. “Indefinite metric and scattering by a domain with a small hole.” *Mathematical Notes*, vol. 58, no. 6, Jan. 1995, pp. 1276–85. *Scopus*, doi:10.1007/BF02304886.
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Kiselev, A., and B. Simon. “Rank one perturbations with infinitesimal coupling.” *Journal of Functional Analysis*, vol. 130, no. 2, Jan. 1995, pp. 345–56. *Scopus*, doi:10.1006/jfan.1995.1074.
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Kiselev, Alexander, and Lenya Ryzhik. *A simple model for asset price bubble formation and collapse*.

Choi, Kyudong, et al. *On the Finite-Time Blowup of a 1D Model for the 3D Axisymmetric Euler
Equations*.

Kiselev, Alexander, and Hang Yang. “Analysis of a Singular Boussinesq Model.” *Research in the Mathematical Sciences*, vol. 6, Springer Verlag.

He, Siming, and Alexander Kiselev. *Small scale creation for solutions of the SQG equation*.