Hamid Hezari
Associate ProfessorDepartment of Mathematics
UC Irvine
Office: Rowland Hall 510J
E-mail: my last name at uci dot edu
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), to appear in Transactions of AMS, arXiv-pdf
26. 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
25. The Dirichlet isospectral problem for trapezoids (with Zhiqin Lu and Julie Rowlett), Journal of Mathematical Physics, Vol. 62, 2021, 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 ℤ2-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 Lp 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. Lp 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 Rn (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
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