# Michael Goldberg

## Professor

## Professor and Department Head

### French Hall

4114

A&S Mathematical Sciences - 0025

## Professional Summary

Personal homepage: https://homepages.uc.edu/goldbeml/

## Education

Ph.D.: University of California at Berkeley 2002 (Mathematics)

A.B.: Princeton University 1997 (Mathematics)

## Research and Practice Interests

Research interests include harmonic analysis and function spaces, in particular the properties of Fourier transforms, and application of these tools to the study of Partial Differential Equations.

## Positions and Work Experience

2020 - Department Head, University of Cincinnati, Cincinnati, OH

2018 - Professor, University of Cincinnati, Cincinnati, OH

2011 -2018 Associate Professor, University of Cincinnati, Cincinnati, OH

2009 -2011 Assistant Professor, University of Cincinnati, Cincinnati, OH

2005 -2009 Assistant Professor, Johns Hopkins University, Baltimore, MD

2002 -2005 Bateman Research Instructor, California Institute of Technology, Pasadena, CA

## Research Support

Grant: #635369 Investigators:Goldberg, Michael 09-01-2019 -08-31-2024 Simons Foundation Fourier Analysis and Dispersive Evolution Equations Role:PI $42,000.00 Active

Grant: #DMS-1700077 Investigators:Goldberg, Michael; Slavin, Leonid; Speight, Gareth 02-01-2017 -01-31-2020 National Science Foundation Collaborative Research: Ohio River Analysis Meetings 2017-2019 Role:PI $28,000.00 Active

Grant: #DMS-1412170 Investigators:Goldberg, Michael; Slavin, Leonid 02-01-2014 -01-31-2017 National Science Foundation Collaborative Research: Ohio River Analysis Meetings 2014-2016 Role:PI $15,408.00 Completed

Grant: #281057 Investigators:Goldberg, Michael 09-01-2013 -08-31-2019 Simons Foundation Dispersive Estimates in Continuous and Discrete Media Role:PI $35,000.00 Completed

Grant: #DMS-1305523 Investigators:Goldberg, Michael; Slavin, Leonid 02-01-2013 -01-31-2015 National Science Foundation The 2013 Ohio River Analysis Meeting Role:PI $10,000.00 Completed

Grant: #DMS-1002515 Investigators:Goldberg, Michael 09-01-2009 -08-31-2013 National Science Foundation Harmonic Analysis Methods Related to the Schrodinger Equation Role:PI $133,640.00 Completed

Grant: #DMS-0600925 07-2006 -06-2009 National Science Foundation Dispersive Estimates for the Schrödinger Equation

Grant: #DMS-2000161 Investigators:Goldberg, Michael; Slavin, Leonid; Speight, Gareth 02-01-2020 -01-31-2023 National Science Foundation Collaborative Research: Ohio River Analysis Meetings 2020-2022 Role:Collaborator $16,000.00 Awarded Level:Federal

## Abbreviated Publications

### Peer Reviewed Publications

Limiting Absorption Principle and Strichartz Estimates for Dirac Operators in Two and Higher Dimensions, *Comm. Math. Phys. ***367** (2019), no. 1, 241-263.

On the Lp Boundedness of Wave Operators for Two-Dimensional Schrödinger Operators with Threshold Obstructions,* J. Funct. Anal.* **274** (2018), no. 7, 2139-2161.

The Helmoholtz Equation with Lp data and Bochner-Riesz Multipliers, *Math Res. Lett.* **23** (2016), no. 6, 1665-1679.

The Klein-Gordon Equation on **Z**2 and the Quantum Harmonic Lattice (with V. Borovyk). *J. Math. Pures Appl.* **107** (2017), no. 6, 667-696.

On the Lp Boundedness of Wave Operators for Four-Dimensional Schrödinger Operators with a Threshold Eigenvalue (with W. Green), *Ann. Henri Poincaré* **18** (2017), no. 4, 1269-1288.

Dispersive Estimates for Higher Dimensional Schrödinger Operators with Threshold Eigenvalues II: The Even Dimensional Case (with W. Green), *J. Spectr. Theory* **7** (2017), no. 1, 33-86.

The Lp Boundedness of Wave Operators for Schrödinger Operators with Threshold Singularities (with W. Green), *Adv. Math.* **303 **(2016), 360-389.

Dispersive Estimates for Higher Dimensional Schrödinger Operators with Threshold Eigenvalues I: The Odd Dimensional Case (with W. Green), *J. Funct. Anal.* **269** (2015), no. 3, 633-682.

Dispersive Estimates for Four Dimensional Schrödinger Operators with Obstructions at Zero Energy (with M.B. Erdogan and W. Green), *Comm. PDE.* **39** (2014), no. 10, 1936-1964

Strichartz Estimates and Maximal Operators for the Wave Equation in **R**3, *J. Funct. Anal.* **266** (2014), no. 3, 1476-1510.

Dispersive Estimates for Schrödinger Operators with Measure-Valued Potentials in **R**^{3},* Indiana Univ. Math. J.* **61** (2012), no. 6, 2123-2141.

Schrödinger Dispersive Estimates for a Scaling-Critical Class of Potentials (with M. Beceanu), *Comm. Math. Phys.* **314** (2012), 471-481.

Strichartz Estimates for Schrödinger Operators with a Non-Smooth Magnetic Potential, Discrete Contin. Dyn. Syst. **31** (2011), no. 1, 109-118.

A Dispersive Bound for Three-Dimensional Schrödinger Operators with Zero Energy Eigenvalues, Comm. PDE **35** (2010), 1610-1634.

Strichartz Estimates for the Schrödinger Equation with Time-Periodic L^{n/2} Potentials, J. Funct. Anal. **256** (2009), 718-746.

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.

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.

Transport in the One-Dimensional Schrödinger Equation, Proc. Amer. Math. Soc. **135** (2007), 3171-3179.

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.

A Counterexample to Dispersive Estimates for Schrödinger Operators in Higher Dimensions (with M. Visan), Comm. Math. Phys. **266** (2006), no. 1, 211-238.

Dispersive Bounds for the Three-Dimensional Schrödinger Equation with Almost Critical Potentials, Geom. and Funct. Anal. **16** (2006), no. 3, 517-536.

Dispersive Estimates for the Three-Dimensional Schrödinger Equation with Rough Potentials, Amer. J. Math. **128** (2006) 731-750.

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.

Dispersive Estimates for Schrödinger Operators in Dimensions One and Three (with W. Schlag), *Comm. Math. Phys.* **251** (2004), no. 1, 157-178.

Matrix *A _{p}* Weights via Maximal Functions, Pac. J. Math.

**211**(2003), 201-220.

Asymptotic Properties of the Vector Carleson Embedding Theorem, Proc. Amer. Math. Soc. **130 **(2002), 529-531.

Vector *A*_{2} Weights and a Hardy-Littlewood Maximal Function (with M. Christ), Trans. Amer. Math. Soc. **353 **(2001), 1995-2002.

## Presentations

### Invited Presentations

Michael Goldberg
(05-17-2016. )
*Functions whose Fourier Transform Vanishes on the Sphere *.Conference in Harmonic Analysis in honor of Michael Christ, University of Wisconsin. Conference. .
Level:International

### Colloquium

Michael Goldberg
(03-19-2019).
*Fourier Restrictions with Derivatives *. Analysis Commons, University of Virginia. Other Institution.
Level:Department

### Paper Presentations

Michael Goldberg, Burak Erdogan and William Green
(11-02-2019. )
*Strichartz estimates for higher-dimensional Schrodinger operators with lower-dimensional potentials *.Gainesville, FL. Conference.
Level:Regional

Michael Goldberg
(04-14-2018. )
*Time-weighted Strichartz Inequalities *.Nashville, TN. Conference.
Level:Regional

Michael Goldberg, Burak Erdogan, William Green
(09-17-2017. )
*A Limiting Absorption Principle for Dirac Operators in Two and Higher Dimensions *.Buffalo, NY. Conference.
Level:Regional

Michael Goldberg, Marius Beceanu
(04-02-2017. )
*Pointwise Bounds for the Three-Dimensional Wave Propagator *.Bloomington, IN. Conference.
Level:Regional

Michael Goldberg
(09-24-2016. )
*Square-Integrable Solutions of the Helmholtz Equation *.Miami University. Conference.
Level:Regional

Michael Goldberg, William Green
(01-06-2016. )
*L ^{p} Bounds for the Schrödinger Equation with a Threshold Eigenvalue *.Seattle, WA. Conference.
Level:National

Michael Goldberg
(12-07-2015. )
*Dirac Points in the Spectrum of Periodic Planar Networks *.Scottsdale, AZ. Conference.
Level:National

Michael Goldberg
(05-28-2015. )
*Counting Cusp Singularities in Two-dimensional Discrete Dispersive Equations *.Drexel University. Other Institution.
Level:Department

Michael Goldberg, William Green
(10-25-2014. )
*Dispersive Estimates for Schrödinger Operators with a Threshold Eigenvalue *.San Francisco, CA. Conference.
Level:Regional

Michael Goldberg
(01-18-2014. )
*Bochner-Riesz Estimates for Functions with Vanishing Fourier Transform *.Baltimore, MD. Conference.
Level:National

(12-07-2013. )
*The Discrete Schroedinger Equation on Triangular Lattices *.Orlando, FL. Conference.
Level:National

Michael Goldberg
(06-29-2013. )
*The Wiener L1 Inversion Theorem in Dispersive PDE *.Euler Institute, Saint Petersburg, Russia. Conference.
Level:International

Michael Goldberg, Vita Borovyk
(03-25-2013. )
*Wave Propagation on Periodic Planar Graphs *.IMACS Conference on Nonlinear Evolution Equations and Wave Phenomena, Athens, GA. Conference.
Level:National

Michael Goldberg, Marius Beceanu
(03-31-2012. )
*Estimates for the Wave Equation with a Rough Potential *.American Mathematical Society Central Sectional Meeting, University of Kansas, Lawrence, KS. Conference.
Level:Regional

## Service

(Graduate Program Director ) Type:Departmental Service Level:Department 08-2017 -08-2020