# Hamid Hezari

Associate ProfessorDepartment of Mathematics

UC Irvine

**Office**: Rowland Hall 510J

# About me

I got my PhD from Johns Hopkins University in 2009. From 2009-2012 I was a CLE Moore instructor at MIT, and I spent the fall of 2010 as a postdoc at the MSRI program on inverse problems. I am currently an associate professor at University of California, Irvine.

My research is in analysis and partial differential equations. I am especially interested in semiclassical/microlocal analysis and its applications in PDE and mathematical physics, in particular spectral geometry and quantum chaos.

# Publications and Preprints

29. Upper bounds on the size of nodal sets for Gevrey and quasianalytic Riemannian manifolds, submitted, arXiv-pdf

28. One can hear the shape of ellipses of small eccentricity (with Steve Zelditch), To appear in *Annals of Mathematics*, January 2023 issue, Vol. 197, No. 1,
arXiv-pdf

27. Centrally symmetric analytic plane domains are spectrally determined in this class (with Steve Zelditch), submitted, arXiv-pdf

26. The Dirichlet isospectral problem for trapezoids (with Zhiqin Lu and Julie Rowlett), *Journal of Mathematical Physics*, Vol. 62, 2021,
arXiv-pdf

25. Eigenfunction asymptotics and spectral rigidity of the ellipse (with Steve Zelditch), *Journal of Spectral Theory*, Vol. 12, special issue in memory of M. Shubin, 2022,
arXiv-pdf

24. On a property of Bergman kernels when the Kähler potential is analytic (with Hang Xu), * Pacific Journal of Mathematics*, Vol. 313, No. 2, 2021,
arXiv-pdf

23. Equidistribution of toral eigenfunctions along hypersurfaces (with Gabriel Rivière), *Revista Mathemática Iberoamericana*, Vol. 36, No. 2, 2019,
arXiv-pdf

22. Quantitative upper bounds for Bergman kernels associated to smooth Kähler potentials (with Hang Xu), *Mathematical Research Letters , Vol. 27, No. 3, 2020,
arXiv-pdf *

21. Off-diagonal asymptotic properties of Bergman kernels associated to analytic Kähler potentials (with Zhiqin Lu and Hang Xu), *International
Mathematics Research Notices*, Vol. 2020, Issue 8, 2020,
arXiv-pdf

20. An appendix of Dynamical spectral rigidity among ℤ_{2}-symmetric strictly convex domains close to a circle by De Simoi, Kaloshin, and Wei (joint with the authors), * Annals of Mathematics*,
Vol. 186, No. 1, 2017, arXiv-pdf

19. Robin spectral rigidity of nearly circular domains with a reflectional symmetry, *Communications in Partial Differential Equations*, Vol. 42, No. 9, 2017,
arXiv-pdf

18. Quantum ergodicity and L^{p} norms of restrictions of eigenfunctions, *Communications in Mathematical Physics*, Vol. 357, No. 3, 2018,
arXiv-pdf

17. Inner radius of nodal domains of quantum ergodic eigenfunctions, * Proceedings of American Mathematical Society*, Vol. 146, No. 11, 2018,
arXiv-pdf

16. Applications of small scale quantum ergodicity in nodal sets, *Analysis and PDE*, Vol. 11, No. 4, 2018,
arXiv-pdf

15. The Neumann isospectral problem for trapezoids (with Julie Rowlett and Zhiqin Lu), * Annales Henri Poincaré *, Vol. 18, No. 12, 2017,
arXiv-pdf

14. Quantitative equidistribution properties of toral eigenfunctions (with Gabriel Rivière). * Journal of Spectral Theory *, Vol. 7, No. 2, 2017, arXiv-pdf

13. L^{p} norms, nodal sets, and quantum ergodicity (with Gabriel Rivière). * Advances in Mathematics*, Vol. 290, 2016, arXiv-pdf

12. Asymptotic expansion of the Bergman kernel via perturbation of the Bargmann-Fock model
(with Casey Kelleher, Shoo Seto, and Hang Xu). * Journal of Geometric Analysis, Vol. 26, No. 4, 2016, * arXiv-pdf

11. Completeness of boundary traces of eigenfunctions (with
Xioalong Han,
Andrew Hassell,
and Steve Zelditch). *Proceedings of
the London Mathematical Society*, Vol. 111, No. 3, 2015, arXiv-pdf

10. A Fulling-Kuchment theorem for the
harmonic oscillator (with Victor
Guillemin). *Inverse Problems*, Vol. 28, No. 4, 2012, arXiv-pdf

9. Inverse problems in spectral
geometry, a survey on inverse spectral problems (with Kiril
Datchev). *Inverse Problems and Applications: Inside Out II*, MSRI Publications, No. 60, 2012, arXiv-pdf

8. A natural lower bound for the size
of nodal sets (with Christopher
Sogge). *Analysis and PDE*, Vol. 5, No. 5, 2012, arXiv-pdf

7. Lower bounds for volumes of nodal
sets: an improvement of a result of Sogge-Zelditch (with Zuoqin
Wang). *AMS Special Issue on Spectral Geometry*, 2012,
arXiv-pdf

6. Resonant uniqueness of radial
semiclassical Schrödinger operators (with Kiril
Datchev). *Applied Mathematics Research eXpress*, Vol. 2012, No. 1, 2012,
arXiv-pdf

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

4. C^{∞
}spectral rigidity of the ellipse (with Steve
Zelditch). *Analysis and PDE*, Vol. 5, No. 5, 2012, arXiv-pdf

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

2. Inverse spectral problems for
Schrödinger operators. *Communications in Mathematical
Physics*, No. 3, 2009, arXiv-pdf

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

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# Teaching at UC Irvine

Math 140B: Elementary Analysis, Spring 2021

Math 140A: Elementary Analysis, Winter 2021 and Spring 2021

Math 3D: Ordinary Differential Equations (Lec A and B), Spring 2020

Math 112B: Introduction to Partial Differential Equations, Winter 2020

Math 2E: Multivariable Calculus, Winter 2019

Math 112B: Introduction to Partial Differential Equations, Winter 2019

Math 147: Complex Analysis, Spring 2018 and Fall 2018

Math 3D: Ordinary Differential Equations, Fall 2017

Math 112A: Introduction to Partial Differential Equations, Fall 2017

Math 140B: Elementary Analysis, Spring 2017

Math 3D: Ordinary Differential Equations, Winter 2017

Math 3D: Ordinary Differential Equations, Fall 2017

Math 112A: Introduction to Partial Differential Equations, Fall 2017

Math 140B: Elementary Analysis, Spring 2017

Math 3D: Ordinary Differential Equations, Winter 2017

Math 2E: Multivariable Calculus, Fall 2016

Math 112A: Introduction to Partial Differential Equations, Fall 2016

Math 2D: Multivariable Calculus, Winter 2016

Math 296: Topics course on Microlocal Analysis, Fall 2015

Math 13: Introduction to Abstract Mathematics, Summer 2015

Math 2D: Multivariable Calculus, Summer 2015

Math 3A: Linear Algebra, Spring 2015

Math 296: Harmonic Analysis, Winter 2015

Math 2D: Multivariable Calculus, Fall 2014

Math 205ABC: Introduction to Graduate Analysis, Fall 2013, Winter 2014, Spring 2014

Math 117: Dynamical Systems, Winter 2013

Math 114: Complex Analysis, Fall 2012

Math 118: Theory of Differential Equations, Fall 2012