Markus Keel
Professor
B.S., Mathematics, University of Chicago
Ph.D., Mathematics, Princeton
Research Interests
PDE, Harmonic Analysis,
Debate
Minnesota PDE Seminar
Teaching, U of M Fall 2021
Honors Mathematics: Math 3592H (Foundations, Sequences and Series, Linear Algebra)
Introduction to Stochastic Processes: Math 5652 (A course developed by my colleagues Professor Wei-Kuo Chen and Professor Arnab Sen at UMN)
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), 805842.
[.ps]
- (with T. Tao) Local and global well posedness of wave maps on R1+1
for rough data, Intl. Math. Res. Notices 21 (1998),
11171156
- (with T. Tao) Small data blowup for semilinear Klein-Gordon equations, Am. J.
Math. 121 (1999), 629669
- (with T. Tao) Endpoint Strichartz inequalities, Am. J. Math. 120
(1998), 955980 [.ps] , [.pdf]
- Global existence for critical power Yang-Mills-Higgs equations in R3+1,
Commun. in PDE 22 (1997), 11671227
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
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