**Benjamin Dodson**

**Professor**

Department of Mathematics

Johns Hopkins University

Baltimore, MD 21218

Office: Krieger 214

Phone: (410) 516-7472

Email: dodson@math.jhu.edu

**Papers: This is a list of research papers that are now published, with links to the paper.**

1. Infrared Photometry of NGC 6791 (with Bruce Carney and Jae - Woo Lee)

2. Global existence for some radial, low regularity nonlinear Schrödinger equations

3. Improved almost Morawetz estimates for the cubic nonlinear Schrödinger equation

4. Global well–posedness and scattering for the defocusing, L^{2} – critical nonlinear Schrödinger equation when d ≥ 3

5. Global well–posedness for the defocusing, quintic nonlinear Schrödinger equation in one dimension for low regularity data

6. Global well–posedness and scattering for the defocusing, cubic nonlinear Schrödinger equation when n = 3 via a linear – nonlinear decomposition

7. Scattering for the radial 3D cubic wave equation (with Andrew Lawrie)

8. A controlling norm for energy – critical Schrödinger maps (with Paul Smith)

9. Scattering for radial, semi – linear super – critical wave equations with bounded critical norm (with Andrew Lawrie)

10. Global well–posedness and scattering for the mass – critical nonlinear Schrödinger equation with mass below the mass of the ground state

11. Global well–posedness and scattering for the defocusing, L^{2} – critical nonlinear Schrödinger equation when d = 1

12. Global well–posedness and scattering for the defocusing, L^{2} – critical nonlinear Schrödinger equation when d = 2

13. Global well–posedness and scattering for the defocusing, mass–critical generalized KdV equation

14. The defocusing quintic NLS in four space dimensions (with Changxing Miao, Jason Murphy, and Jiqiang Zheng)

15. On scattering for small data of 2+1 dimensional equivariant Einstein-wave map system (with Nishanth Gudapati)

16. A new proof of scattering below the ground state for the 3D radial focusing cubic NLS (with Jason Murphy)

17. Global well-posedness and scattering for the radial, defocusing cubic wave equation with almost sharp initial data

18. The profile decomposition for the hyperbolic Schrödinger equation (with Jeremy Marzuola, Benoit Pausader, and Daniel Spirn)

18a. Erratum to the profile decomposition for the hyperbolic Schrödinger equation (with Jeremy Marzuola, Benoit Pausader, and Daniel Spirn)

19. A new proof of scattering below the ground state for the non-radial focusing NLS (with Jason Murphy)

20. Global well-posedness and scattering for the radial, defocusing cubic wave equation with initial data in a critical Besov space

21. Almost sure local well-posedness and scattering for the 4D cubic nonlinear Schrödinger equation (with Jonas Lührmann and Dana Mendelson)

22. Global well-posedness and scattering for the focusing, cubic Schrödinger equation in dimension d = 4

23. Global well-posedness and scattering for nonlinear Schrödinger equations with algebraic nonlinearity when d = 2, 3 and u_{0} is radial

24. Global well-posedness for the defocusing, cubic, nonlinear wave equation in three dimensions for radial initial data in H^{s} ˣ H^{s-1}, s > ½

25. Scattering below the ground state for the 2D radial nonlinear Schrödinger equation (with Anudeep Kumar Arora and Jason Murphy)

26. Almost sure scattering for the 4D energy-critical defocusing nonlinear wave equation with radial data (with Jonas Lührmann and Dana Mendelson)

27. The nonlinear Schrödinger equation on **Z** and **R** with bounded initial data: Examples and conjectures (with Thomas Spencer and Avy Soffer)

28. Scattering for defocusing energy subcritical nonlinear wave equations (with Andrew Lawrie, Dana Mendelson, and Jason Murphy)

29. Global well-posedness for the logarithmically energy-supercritical nonlinear wave equation with partial symmetry (with Aynur Bulut)

30. Global well-posedness for the cubic nonlinear Schrödinger equation with initial data lying in L^{p}-based Sobolev spaces (with Thomas Spencer and Avy Soffer)

31. The L^{2} sequential convergence of a solution to the one-dimensional, mass-critical NLS above the ground state

32. Scattering for the radial defocusing cubic nonlinear wave equation with initial data in the critical Sobolev space

33. The L^{2} sequential convergence of a solution to the mass-critical NLS above the ground state

34. Instability of the soliton for the focusing, mass-critical generalized KdV equation (with Cristian Gavrus)

35. Global well–posedness for the defocusing, cubic nonlinear Schrödinger equation with initial data in a critical space

36. A determination of the blowup solutions to the focusing NLS with mass equal to the mass of the soliton

Arxiv preprints may be found here

**Book:**

Defocusing nonlinear Schrödinger equations

**PhD Thesis: **

Caustics and the indefinite signature Schrödinger equation, linear and nonlinear

**Keynote presentation:**

Scattering for the defocusing, cubic nonlinear wave equation

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