Conformal Geometry, Analysis, and Physics

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This award provides support for the conference "Conformal Geometry, Analysis, and Physics" to be held in Seattle from June 13-17, 2022. The field of conformal geometry has had rich interactions with both geometric analysis and physics, especially high-energy and condensed-matter physics, over the past three decades. The benefits have been bidirectional in both cases: conformal geometry has led to the development of new analytic tools infused by geometric intuitions, which in turn lead to the solution of important geometric problems. Similarly, physics is a source both of new problems and of important insights, while conformal geometry provides crucial tools in the solution of physical problems. This conference will bring together experts from all of these fields to share and discuss their research and benefit from each other's perspectives and tools. It is expected that the conference will stimulate further development in all three fields and cooperation across many kinds of boundaries. Facilitating entry of early-career researchers into dialog with all three areas is a particular goal for this event. A poster session will be held for students.Conformal geometry is the geometry of spaces where angles are defined, but not lengths. It has had a long and, recently, fast-growing relevance in physics, where it is a tool that provides new perspectives on many old phenomena. Conversely, physics has been a rich source of insights and problems in conformal geometry. For many years now, conformal geometry itself has provided some of the most compelling problems in geometric analysis, while techniques from analysis, scattering theory, and partial differential equations have enabled tremendous progress in the field. The primary goal of the conference is to bring together researchers from the three title areas whose work overlaps, in order to disseminate progress, share interesting problems, build relationships, and broaden perspectives. The conference will allow exposure to relevant state-of-the-art techniques in conformal geometry, analysis, and physics to be shared with other interested practitioners in each field. It will foster international collaboration between the US and other countries, and also collaboration between mathematicians and physicists. Junior participants will gain valuable insights, and relationships with more senior practitioners that may shape both their career and their mathematical (or physical) perspectives. Opportunity will be given for them to present their own work, and collaboration opportunities will exist between researchers at all levels. Most of the funding will be used to support junior mathematicians. Substantial effort will be made in recruiting women and members of other underrepresented groups in mathematics. The conference website is at https://personal.utdallas.edu/~sxm190098/graham65/ .This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.