Hamid Hezari

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Hamid Hezari

Associate Professor
Department of Mathematics
UC Irvine

Office: Rowland Hall 510J
E-mail: h-e-z-a-r-i-AT-m-a-t-h.u-c-i.e-d-u
 

Publications


23. Equidistribution of toral eigenfunctions along hypersurfaces (with Gabriel Rivière), to appear in Revista Mathemática Iberoamericana, arXiv-pdf




22. Quantitative upper bounds for Bergman kernels associated to smooth Kähler potentials (with Hang Xu), to appear in Mathematical Research Letters, arXiv-pdf


21. Off-diagonal asymptotic properties of Bergman kernels associated to analytic Kähler potentials (with Zhiqin Lu and Hang Xu), to appear in IMRN, 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


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

 

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.