CLE Moore Instructor

Department of Mathematics

MIT

77 Mass Ave

Cambridge, MA 02139

Mentor: Richard Melrose

**Office**: 2-363B **E-mail**:
hezari@math.mit.edu

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**About me**

I received my PhD from Johns Hopkins in 2009. My adviser was Steve Zelditch. Since then I have been a CLE Moore instructor at MIT, and I spent the fall of 2010 as a postdoc at the MSRI program on inverse problems. This fall, 2011, I am applying for academic jobs.

My research is in partial differential equations and geometric analysis, and I am especially interested in inverse problems and spectral geometry.My research is supported in part by NSF grant DMS-0969745.

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1. C^{∞ } spectral rigidity of the anisotropic harmonic oscillator. In preparation

2. A Fulling-Kuchment theorem for the harmonic oscillator (with Victor Guillemin). Submitted, arXiv-pdf

3. Inverse problems in spectral geometry, a survey on inverse spectral problems (with Kiril Datchev). To appear in *Inverse Problems and Applications: Inside Out II *, arXiv-pdf

4. A natural lower bound for the size of nodal sets (with Christopher Sogge). To appear in *Analysis & PDE*, arXiv-pdf

5. Lower bounds for volumes of nodal sets: an improvement of a result of Sogge-Zelditch (with Zuoqin Wang). To appear in *AMS Proceedings on Spectral Geometry*, arXiv-pdf

6. Resonant uniqueness of radial semiclassical Schrödinger operators (with Kiril Datchev). To appear in *Applied Mathematics Research eXpress*, arXiv-pdf

7. Spectral uniqueness of radial semiclassical Schrödinger operators (with Kiril Datchev and Ivan Ventura ). *Mathematical Research Letters*, Vol. 18, No. 3, pp. 521–529, 2011, arXiv-pdf

8. C^{∞ } spectral rigidity of the ellipse (with Steve Zelditch). Revise and submit, *Analysis and PDE*, arXiv-pdf

9. Inverse spectral problems for (Z/2Z)^{n}-symmetric
domains in R^{n}
(with Steve Zelditch). *GAFA* Vol. 20, No. 1, pp. 160--191, 2010, arXiv-pdf

10. Inverse spectral problems for Schrödinger operators. *Communications in Mathematical Physics*,
No. 3, pp. 1061--1088, 2009, arXiv-pdf

11. Complex zeros of eigenfunctions of 1-dimensional Schrödinger
Operators. *International Mathematics Research Notices*, No.3, article ID: rnm148, 2008,
arXiv-pdf

Eigenvalues and eigenfunctions of Schrödinger operators: Inverse spectral theory and the zeros of eigenfunctions. Ph.D. Thesis, The Johns Hopkins University, 2009

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18.100C- Real Analysis, **Fall 2011

18.06- Linear Algebra, Spring 2011

**
18.024- Multivariable Calculus with Theory , **Spring 2010

18.03- Differential Equations, Fall 2009

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