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Michael Goldberg Assistant Professor
Office: 313 Krieger Hall Phone: 410-516-7406 Fax: 410-516-5549 E-mail: mikeg   @   math   . jhu   . edu	Mailing address: Dept. of Mathematics Johns Hopkins University Baltimore, MD 21218

Research
I use techniques from Fourier analysis to study partial differential equations.
(I also use partial differential equations as an excuse to do Fourier analysis!)

My current project is to prove linear dispersive estimates for the Schrödinger equation in a variety of settings,
with an eye toward understanding the dynamics of NLS evolution near standing wave solutions.

These slides from some of my recent talks discuss specific problems and results.
Some of this work is supported by a National Science Foundation grant (DMS-0600925).

For the past several years, I have organized the Analysis and PDE Seminar at Johns Hopkins.

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Teaching
Office Hours, Spring 2009: Thursdays, 10am - noon, 313 Krieger Hall.
Courses taught at Johns Hopkins:

• Math 113 - Honors Calculus II [Fall 2005]
• Math 201 - Linear Algebra [Spring 2006]
• Math 302 - Differential Equations with Applications [Spring 2006]  [Spring 2008]
• Math 306 - Honors Differential Equations [Spring 2009]
• Math 415 - Honors Analysis I [Fall 2007]  [Fall 2008]
• Math 416 - Honors Analysis II [Spring 2007]
• Math 443 - Fourier Analysis [Fall 2006]
• Math 640 - Spectral Theory [Spring 2007]  [Spring 2009]

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Publications and Preprints

• A Dispersive Bound for Three-Dimensional Schrödinger Operators with Zero Energy Eigenvalues, Preprint 2008.  [dvi]  [ps]  [pdf] 
• Strichartz Estimates for Schrödinger Operators with a Non-Smooth Magnetic Potential, Preprint 2008.   [dvi]  [ps]  [pdf] 
• Strichartz Estimates for the Schrödinger Equation with Time-Periodic L^n/2 Potentials, J. Funct. Anal. 256 (2009), 718-746.  [dvi]  [ps]  [pdf] 
• Strichartz and Smoothing Estimates for Schrödinger Operators with Almost Critical Magnetic Potentials in Three and Higher Dimensions (with M. B. Erdogan and W. Schlag), Forum Math. 21 (2009), no. 4, 687-722.   [dvi]  [ps]  [pdf] 
• Strichartz and Smoothing Estimates for Schrödinger Operators with Large Magnetic Potentials in R³ (with M. B. Erdogan and W. Schlag), J. Eur. Math. Soc. 10 (2008), no. 2, 507-531.   [dvi]  [pdf] 
• Transport in the One-Dimensional Schrödinger Equation, Proc. Amer. Math. Soc. 135 (2007), 3171-3179.   [dvi]  [pdf] 
• Counterexamples of Strichartz Inequalities for Schrödinger Equations with Repulsive Potentials (with L. Vega and N. Visciglia), Intl. Math. Res. Not. 2006 (2006), Article ID 13927, 16pp.   [dvi]  [pdf] 
• A Counterexample to Dispersive Estimates for Schrödinger Operators in Higher Dimensions (with M. Visan), Comm. Math. Phys. 266 (2006), no. 1, 211-238.  [dvi]  [pdf] 
• Dispersive Bounds for the Three-Dimensional Schrödinger Equation with Almost Critical Potentials, Geom. and Funct. Anal. 16 (2006), no. 3, 517-536.  [dvi]  [ps]  [pdf]
• Dispersive Estimates for the Three-Dimensional Schrödinger Equation with Rough Potentials, Amer. J. Math. 128 (2006) 731-750.   [dvi]  [ps]  [pdf]
• A Limiting Absorption Principle for the Three-Dimensional Schrödinger Equation with L^p Potentials (with W. Schlag), Intl. Math. Res. Not. 2004:75 (2004), 4049-4071.  [dvi]  [ps]  [pdf]
• Dispersive Estimates for Schrödinger Operators in Dimensions One and Three (with W. Schlag), Comm. Math. Phys. 251 (2004), no. 1, 157-178.  [dvi]  [ps]  [pdf]
• Matrix A_p Weights via Maximal Functions, Pac. J. Math. 211 (2003), 201-220.  [dvi]  [ps]  [pdf]
• Asymptotic Properties of the Vector Carleson Embedding Theorem, Proc. Amer. Math. Soc. 130 (2002), 529-531.  [dvi]  [ps]  [pdf]
• Vector A₂ Weights and a Hardy-Littlewood Maximal Function (with M. Christ), Trans. Amer. Math. Soc. 353 (2001), 1995-2002.  [dvi]  [ps]  [pdf]

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Education
AB., Mathematics, Princeton University, 1997
Ph.D., Mathematics, University of California, Berkeley, 2002

Here is my full Curriculum Vitae .

Fun Stuff

U.S. National Weather Service	Geyser Observation and Study Association
Current weather watches and warnings from the NWS	Old Faithful Webcam from the National Park Service in Yellowstone

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