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Michael GoldbergAssistant 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.

**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]**

- 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
**R**^{3}(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*Potentials (with W. Schlag), Intl. Math. Res. Not.^{p}**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*Weights via Maximal Functions, Pac. J. Math._{p}**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
*A*_{2}Weights and a Hardy-Littlewood Maximal Function (with M. Christ), Trans. Amer. Math. Soc.**353**(2001), 1995-2002. [dvi] [ps] [pdf]

**Education**

AB., Mathematics,
Princeton University, 1997

Ph.D., Mathematics, University of
California, Berkeley, 2002

Here is my full
**Curriculum Vitae
**.

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