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Zhiyan ZHAO--赵之彦


Contact information:

Office: 4.819, Laboratoire J. A. Dieudonné

Université de Nice-Sophia Antipolis, Parc Valrose

06108 Nice Cedex 02, France

Email: zhiyan.zhao@unice.fr


Research Interests:

· Perturbation theory for infinite-dimensional Hamiltonian systems, in particular:

1. Long-time behavior of Hamiltonian PDEs

2. Infinite-dimensional KAM theory

· Spectral theory of Schrödinger operator, in particular:

1. Anderson localization in quasi-crystal models

2. Reducibility and almost reducibility of Schrödinger cocycle

3. Transport property of quantum dynamics


Professional Experience:

· 2016.9.- : Maître de conférences, Université de Nice-Sophia Antipolis(Parc Valrose), France

· 2015.9.-2016.8.: Postdoctral fellow(contract A.N.R., Responsable: Laurent STOLOVITCH), Laboratoire J. A. Dieudonné, France

· 2014.9.-2015.8.: Postdoctral fellow(contract F.S.M.P., Responsable: Hakan ELIASSON), Institut de Mathématique de Jussieu-Paris Rive Gauche, France

· 2013.9.-2014.8.: Postdoctral fellow(contract A.N.R., Responsable: Jean-Christophe YOCCOZ), Collège de France, France

· 2009.9.-2013.6.: Teaching assistant, Nanjing University, China


Education:

· 2010.9.-2013.6.: Ph.D. Mathematics, Nanjing University, China.

Advisor: Jiangong YOU (also directed by Jiansheng GENG)

Thesis: Anderson localization in disordered dynamical systems. English version Chinese version

Date of thesis defense: May 9 2013

· 2008.9.-2010.6.: Master on <<Probability and Statistics>>(transfer to Ph.D. without diploma), Nanjing University, China.

· 2004.9.-2008.6.: B.S. Mathematics, Jiangsu Normal University, China.


Publication:

· Z. Zhang and Z. Zhao: Ballistic transport and absolute continuity of one-frequency quasi-periodic Schrödinger operators. Commun. Math. Phys. 351, 877-921(2017). Journal arxiv: 1512.02195

· Z. Zhao: Ballistic transport in one-dimensional quasi-periodic continuous Schrödinger equation. J. Diff. Eqs. 262, 4523-4566(2017). Journal arxiv:1604.00210

· Z. Zhao: Ballistic motion in one-dimensional quasi-periodic discrete Schrödinger equation. Commun. Math. Phys. 347, 511–549(2016). Journal arxiv:1507.08909

· J. Geng and Z. Zhao: Reducibility of one-dimensional quasi-periodic Schrödinger equations. J. Math. Pures Appl. 104, 436453(2015). Journal Article

· J. Geng, J. You and Z. Zhao: Localization in one-dimensional quasi-periodic nonlinear systems. Geom. And Func. Anal. 24, 116–158(2014). Journal Article

· J. Geng and Z. Zhao: Quasi-periodic solutions for one-dimensional discrete nonlinear Schrödinger equations with tangent potential. Siam. J. Math. Anal. 45(6), 3651–3689(2013). Journal Article

· S. Zhang and Z. Zhao: Diffusion bound and reducibility for discrete Schrödinger equations with tangent potential. Front. Math. China, 7(6), 1213–1235(2012). Journal Article

· Z. Zhao and J. Geng: Linearly stable quasi-periodic breathers in a class of random Hamiltonian systems. J. Dyn. Diff. Eqs., 23, 961–997(2011). Journal Article


Talk:

· October 25 2016, Seminario, Università degli studi di Milano, Milan, Italy

· May 10 2016, Séminaire de Systèmes dynamiques, Université d'Avignon, Avignon, France

· March 4 2016, Séminaire d'analyse, Université de Nantes, Nantes, France

· January 25--29 2016, Winter School on Dynamics and PDE's, St. Étienne de Tinée, Nice, France

· December 16--18 2015, Workshop Localization and reducibility in Hamiltonian PDE and Quantum Mechanics, Università degli studi di Milano, Milan, Italy

· July 20--24 2015, Workshop on Dynamische Systeme, Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany

· June 3--8 2015, Conference Hamiltonian systems and their applications, Euler International Mathematical Institute, St. Petersburg, Russia

· April 3 2015, Séminaire de Systèmes Dynamiques, Collège de France, Paris, France

· January 27 2015, Séminaire Dynamique et Géométrie, Laboratoire J. A. Dieudonné, Nice, France

· February 14 2014, Séminaire de Systèmes Dynamiques, Collège de France, Paris, France

· March 16--20 2013, International Conference on Dynamics of Differential Equations, Georgia Institute of Technology, Atlanta, USA


Teaching:

· 2017-2018: Université de Nice-Sophia Antipolis

 CM+TD: Analyse 2(L2PC+SF)

· 2016-2017: Université de Nice-Sophia Antipolis

 TD: Analyse 1(L1) 40H, Responsable: Francesca RAPETTI

 TD: Mathématique pour la Biologie(L1) 25H, Responsable: Andreas HÖRING

 TD: Analyse 2(L2) 40H, Responsable: Nicole SIMPSON

 CM+TD: Modélisation(L2MASS) 40H

· 2015-2016: Université de Nice-Sophia Antipolis

 Colles: Algèbre 2(L2) 10H, Responsable: Adam PARUSINSKI

 TD: Algèbre 1(L1) 40H, Responsable: Hervé DILLINGER