Professor

B.S., Mathematics, University of Chicago

Ph.D., Mathematics, Princeton

PDE, Harmonic Analysis, Debate

Minnesota PDE SeminarMath 5525: Introduction to Differential Equations

Math 3593H: Honors Mathematics

Math 3592H: Honors Calculus (Multivariable Calculus and Analysis)

- 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
**R**^{1+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** - (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
**R**^{3+1},*Commun. in PDE***22**(1997), 1167–1227

Email: mylastname_at_math.umn.edu

Phone: (612)-624-6341

Department of Mathematics

University of Minnesota

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206 Church St. S.E.

Minneapolis, MN 55455

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