The ``Conference: Spectral Theory and Partial Differential Equations'' will be held June 17-21, 2013 at the University of California-Los Angeles. The roots of microlocal analysis,one of the main tools employed in the conference subject area, go back to the beginning of the twentieth century, but its systematic development began about fifty years ago with the theories of Pseudodifferential Operators and Fourier Integral Operators. Since then these theories have revolutionized the subject of partial differential equations. For example, they have played decisive roles in finding the Atiayh-Singer formula for the index of an elliptic operator and in solving the Weyl conjecture about the distribution of eigenvalues for elliptic operators on manifolds, and they provided the precise tools needed for studying the propagation of singularities for solutions of hyperbolic equations on manifolds. Though microlocal analysis has been an important part of linear PDE theory, it has also been successfully applied to non-linear equations as well and there are numerous connections of microlocal analysis to spectral theory, scattering theory, and inverse problems.
This mathematics research conference will bring together leading experts in partial differential equations and it will consider a wide variety of research topics in differential equations. The conference will increase communication among mathematicians from different specialties and it will accelerate research progress in several fields. The organizers plan to publish the talks presented on the conference in a dedicated volume of the series Contemporary Mathematics published by the American Mathematical Society. Special efforts will be made to bring graduate students and postdoctoral fellows to the conference and thereby to stimulate the research of future mathematicians.
" was held at the UCLA Mathematics Department from June 17, 2013 to June 21, 2013. There were 57 registered participants. These included ,14 were graduate students, from UCLA and from other universities, and 10 postdoctoral fellows,also from UCLA and other universities. Invited hour-long addresses were presented by 21 visitors, 2 from UCLA, 5from other universities in California, and 10 from European universities. Partial Differential Equations is a very broad research area, and the talkswere quite varied. We mention four key topics covered by several of thespeakers: On the spectral theory of partial differential operators, there wereseven talks, by Dyatlov, Guillot, Helffler, Ivree, Melrose, Robert anZelditch. Six talks on inverse problems were given by Belishev, Imanuvilov, Isozaki, Nachman, Vasy and Yamamoto. Crandall, Helton, Liu and Sylvester gave talks about the applications of PDE to geometry and on estimates of solutions. Talks on long time behavior of nonlinear equations were given by Tao, Tataru, Visan and Zworski. In spite of the variety of topics, there was considerable discussion and exchange of ideas among the participants, including participants from different specialities. The Conference Proceedings will be published by the American Mathematical Society, in its series Contemporary Mathematics.Several submitted papers are now being refereed. G. Eskin, L. Friedlander, J. Garnett, T. Tao
