Hamid Hezari

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Hamid Hezari

Associate Professor
Department 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), 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 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. Cspectral 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