Markus Keel
Professor

B.S., Mathematics, University of Chicago
Ph.D., Mathematics, Princeton

Research Interests

PDE, Harmonic Analysis, Debate

Teaching, U of M Fall 2021

Papers, click to view

• Global well-posedness of the Maxwell-Klein-Gordon equation below the energy norm (with T. Roy and T. Tao) Discrete Cont. Dyn. Syst. 30, 573--621 (2011). [.ps][.pdf][.dvi]
• Tranfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation (with J. Colliander, G. Staffilani, H. Takaoka, and T. Tao), Inventiones Math. , 181 (2010), 31--113. [.pdf]
• Resonant decompositions and the I-method for cubic nonlinear Schrodinger equations on R ^2 (with J. Colliander, G. Staffilani, H. Takaoka, and T. Tao) , Discrete Contin. Dyn. Syst. 21 (2008), no. 3, 665--686. [.ps][.pdf][.dvi]
• Global well-posedness and scattering for the energy-critical nonlinear Schrödinger equation in R^3 (with J. Colliander, G. Staffilani, H. Takaoka, and T. Tao) Annals of Math. 167, No. 3 (2008), 767--865. [.ps][.pdf][.dvi]
• Symplectic non-squeezing for the KdV flow (with J. Colliander, G. Staffilani, H. Takaoka, and T. Tao) Acta Math. 195 (2005), 197--252. [.pdf]
• (with H. Smith and C.D. Sogge) Almost Global Existence for Quasilinear Wave Equations in Three Space Dimensions , J. Amer. Math. Soc. 17 (2004), no. 1, 109--153.
• Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on R^3 (with J. Colliander, G. Staffilani, H. Takaoka, and T. Tao) Comm. Pure and Applied Mathematics, 57 (2004), 987--1014. [.ps]
• Multilinear estimates for periodic KdV equations, and applications (with J. Colliander, G. Staffilani, H. Takaoka, and T. Tao) Journal of Functional Analysis, 211 (2004), 173--218.[.ps]
• Polynomial upper bounds for the orbital instability of the 1d cubic NLS below the energy norm (with J. Colliander, G. Staffilani, H. Takaoka, and T. Tao) Discrete and Cont. Dyn. Systems, 9 (2003), 31--54. [.ps]
• Polynomial upper bounds for the instability of the Nonlinear Schroedinger equation below the energy norm (with J. Colliander, G. Staffilani, H. Takaoka, and T. Tao) Comm. on Pure Appl. Anal. 2 (2003), 33--50. [.pdf]
• Sharp global well-posedness for KdV and modified KdV on R and T (with J. Colliander, G. Staffilani, H. Takaoka, and T. Tao) J. Amer. Math. Soc. 16 (2003), no. 3, 705--749. [.ps]
• Existence globale et diffusion pour l'équation de Schrödinger nonlinéaire répulsive cubique sur R^3 en dessous l'espace d'énergie (with J. Colliander, G. Staffilani, H. Takaoka, and T. Tao) Proceedings of the Forges Les Eaux Conference on PDE, 2002. [.ps]
• Almost Conservation Laws and Global Rough Solutions to a Nonlinear Schrodinger Equation (with J. Colliander, G. Staffilani, H. Takaoka, and T. Tao) Math. Res. Letters 9 (2002), no. 5-6, 659--682 [.ps]
• (with H. Smith and C.D. Sogge) Global existence for a quasilinear wave equation outside of star-shaped domains, Journal of Functional Analysis 189 (2002), 155-226.
• A refined global well-posedness result for Schrodinger equations with derivatives (with J. Colliander, G. Staffilani, H. Takaoka, and T. Tao) Siam J. Math. Anal. 34 (2002) 64-86 [.ps]
• (with H. Smith and C.D. Sogge) Almost global existence for some semilinear equations, J. d'Anal. Math. 87, (2002), 265--279.
• Global well-posedness for KdV in Sobolev Spaces of negaitve index (with J. Colliander, G. Staffilani, H. Takaoka, and T. Tao) Electron. Journ. Diff. Eq., 2001 [.ps]
• Global well-posedness for Schrodinger equations with derivative (with J. Colliander, G. Staffilani, H. Takaoka, and T. Tao) Siam J. Math. Anal.,33 (2001), 649--669. [.ps]
• (with H. Smith and C.D. Sogge) On global existence for nonlinear wave equations outside convex obstacles, Am. J. Math 122 (2000), 805–842.   [.ps]
• (with T. Tao) Local and global well posedness of wave maps on R¹⁺¹ for rough data, Intl. Math. Res. Notices 21 (1998), 1117–1156 
• (with T. Tao) Small data blowup for semilinear Klein-Gordon equations, Am. J. Math. 121 (1999), 629–669 
• (with T. Tao) Endpoint Strichartz inequalities, Am. J. Math. 120 (1998), 955–980  [.ps] , [.pdf]
• Global existence for critical power Yang-Mills-Higgs equations in R³⁺¹, Commun. in PDE 22 (1997), 1167–1227 

Contact Information

Email: mylastname_at_.umn.edu
Phone: (612)-624-6341
Department of Mathematics
University of Minnesota
127 Vincent Hall
206 Church St. S.E.
Minneapolis, MN 55455

Click here to get a listing of M. Keel's papers from the AMS MathSciNet with links to Mathematical Reviews.
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