Alexander Kiselev

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Alexander "Alex" Kiselev is an American mathematician.

Kiselev studied physics at the State University of Saint Petersburg with a degree in 1992 and received his doctorate at Caltech with Barry Simon in 1996 (Absolutely Continuous Spectrum of One-Dimensional Schrödinger Operators with Slowly Decreasing Potentials). As a post-doctoral student he was at MSRI and from 1997 to 1999 Dickson Instructor at the University of Chicago , where he became Assistant Professor in 1999. He became Associate Professor in 2002 and Professor at the University of Wisconsin-Madison in 2005 and Professor at Rice University in 2014 , where he is Edgar Odell Lovett Professor of Mathematics.

In 2004 he was at the Institute for Advanced Study , 1995/96 at IHES

He deals with partial differential equations, especially the spectral theory of Schrödinger operators, hydrodynamics (including evidence of blow up in some one-dimensional models of the three-dimensional Euler equations and in the Burgers equation with fractional dissipation), mathematical biology and reaction-diffusion equations (for example in chemotaxis or fire). In 2001 he solved one of the Simon problems (existence of a continuous spectrum of the Schrödinger operator with slowly decaying potentials). His work on global well-being for the critical two-dimensional dissipative quasi-geostrophic equation has also been widely cited.

For 2018 he is invited speaker at the International Congress of Mathematicians in Rio de Janeiro and 2006 invited speaker at the International Congress on Mathematical Physics in Rio. In 2012 he was a Guggenheim Fellow and in 2001 a Sloan Fellow.

Fonts (selection)

  • with Tam Do, Xiaoquian Xu: Stability of Blow Up for a 1D model of Axisymmetric 3D Euler Equation, Arxiv 2016
  • with Lenya Ryzhik: Biomixing by chemotaxis and efficiency of biological reactions: the critical reaction case, J. Math. Phys., Volume 53, 2012, p. 115609
  • with L. Ryzhik: Biomixing by chemotaxis and enhancement of biological reactions, Communications in PDE, Volume 37, 2012, pp. 298-318
  • with Fedor Nazarov, Roman Shterenberg: Blow up and regularity for fractal Burgers equation, Arxiv 2008
  • with F. Nazarov, A. Volberg: Global well-posedness for the critical 2D dissipative quasi-geostrophic equation, Inventiones Mathematicae, Volume 167, 2007, pp. 445–453, Arxiv
  • with L. Ryzhik: Enhancement of the traveling front speeds in reaction-diffusion equations with advection, Annales de l'IHP Analyze non linéaire, Volume 18, 2001, pp. 309-358
  • with Michael Christ: Maximal functions associated to filtrations, Journal of Functional Analysis, Volume 179, 2001, pp. 409-425
  • with Rowan Killip, Y. Last: Dynamical upper bounds on wavepacket spreading, American J. Math., Vol. 125, 2003, pp. 1165-1198, Arxiv
  • with P. Constantin, A. Oberman, L. Rhyzik: Bulk Burning Rate in Passive – Reactive Diffusion, Archive for rational mechanics and analysis, Volume 154, 2000, pp. 53–91, Arxiv
  • with Yoram Last: Solutions, spectrum and dynamics of Schrödinger operators on infinite domains, Duke Math. Journal, Volume 102, 2000, pp. 125-150, Arxiv
  • with M. Christ: Absolutely continuous spectrum for one-dimensional Schrödinger operators with slowly decaying potentials: some optimal results, Journal of AMS, Volume 11, 1998, pp. 771-797, Arxiv
  • with Y. Last, Barry Simon : Modified Prüfer and EFGP transforms and the spectral analysis of one-dimensional Schrödinger operators, Commun. Math. Phys., Vol. 194, 1998, pp. 1-45
  • Stability of the absolutely continuous spectrum of Schrödinger operators under slowly decaying perturbations and ae convergence of integral operators, Duke Math. J., Volume 94, 1998, pp. 619-649
  • with M. Christ, C. Remling: The absolutely continuous spectrum of one-dimensional Schrödinger operators with decaying potentials, Math. Res. Lett., Volume 4. 1997, pp. 1-5
  • Absolutely continuous spectrum for one-dimensional Schrödinger operators and Jacobi matrices with slowly decreasing potentials, Commun. Math. Phys., Vol. 179, 1996, pp. 377-400

Web links

Individual evidence

  1. ↑ Alexander Kiselev in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ^ Problem 7 of the list from 2000
  3. ↑ Kiselev, Imbedded Singular Continuous Spectrum for Schrödinger Operators, J. of the AMS, Volume 18, 2005, pp. 571–603, Arxiv 2001
personal data
SURNAME Kiselev, Alexander
ALTERNATIVE NAMES Kiselev, Alex (nickname)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH 20th century