Workshop:Facets of Integrability: Random Patterns, Stochastic Processes, Hydrodynamics, Gauge Theories and Condensed Matter Systems-the Simons Ctr for Geometry&Physics 1/21-27/

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This is a proposal for partial funding for an international workshop "Facets of integrability: random patterns, stochastic processes, hydrodynamics,gauge theories and condensed matter systems" at the Simons Center for Geometry and Physics in January 21-27, 2013. The main goal of the workshop is to establish and investigate relations between random processes and mathematical structures known in classical and quantum integrability. The workshop will focus on various applications of techniques of integrable non-linear systems to random matrices, Dyson diffusion, and counting problems of various geometrical objects arising in random processes, among other topics. The field of integrability is known for being at the interface between mathematics and physics. The influence flows in both directions, with mathematical techniques and ideas contributing crucially to major advances in the theory of integrability. The workshop will bring together mathematicians and physicists who work on ideas related to these fields. The participants will be prominent scientists, young researchers, and students from all over the world. The Simons Center is most suitable for hosting the proposed workshop. It is a research center devoted to bringing mathematicians and physicists together to further fundamental knowledge in geometry and theoretical physics, especially knowledge at the interface of these two disciplines. For broader impact the results presented at the workshop will be recorded and disseminated through a web site of the Simons Center for Geometry and Physics, which is a very natural place to host such a workshop, being located in close proximity to Mathematics and Physics departments of Stony Brook University and to the Yang Institute for Theoretical Physics, with a tradition of excellence in the field of integrability. The main idea of the workshop is to bring together people working in different fields. The cross-fertilization of different fields provides a nice environment for training graduate students and postdocs. Junior researchers will be especially encouraged to participate using NSF support to pay for their for travel and lodging. Supporting the travel of young researchers and graduate students to such a conference where scientists from different scientific fields, old and young, prominent and just beginning, are spending a week in an inspiring and congenial environment will, as it has done so in the past, inspire many beginning researchers, including minorities and members from the underrepresented groups. By prompt advertising and by offering partial travel support it will significantly increase the participation of young students and researchers.