Conference on Analysis, Dynamics, Geometry, and Probability

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This award supports participation in the workshop "Analysis, Dynamics, Geometry, and Probability" held at the Simons Center for Geometry and Physics (SCGP, located in Stony Brook, NY) on March 2-6, 2020. Although the central questions studied in these fields are different, they have had fruitful interaction, and each field has benefited from developments in the others. While some of these connections are centuries old, there have been exciting developments in recent years. The award will allow a diverse group of mostly early-career mathematicians to interact with more established researchers. Bringing together this group will provide an excellent opportunity for interaction, shared insight, and further development. The organizers expect this to be a valuable educational opportunity as well as a research conference. Holding this conference at the SCGP will make it accessible and visible to the physics community, leading to interactions that might not occur as readily otherwise.The workshop will bring together experts from interconnected fields. One example is the connection between Brownian motion, harmonic measure, analysis of singular integrals, and geometric properties of domains. This topic relates how a randomly-moving particle sees the boundary of the region in which it moves, the equilibrium charge distribution on the boundary of this region, and classical questions in analysis. Another example concerns function theory and dynamical systems: which geometric properties of functions are most important in studying the associated dynamical system formed by the iterates of the function, and on the other hand, what can the dynamical system tell us about the geometry of the initial function? The speakers include prominent researchers from a wide range of areas, including computer science, applied mathematics, dynamical systems, probability, analysis, and geometry. Many speakers have a history of making good use of such interchanges for groundbreaking work, some with important practical applications. Some specific examples are Ingrid Daubechies’ work on wavelets and their numerous applications (for example, image compression), Peter Jones’ work on diffusion geometry for data analysis, Svitlana Mayboroda’s work on localization of waves (used in LED light design), and Assaf Naor’s work on metric embeddings and algorithms, with applications in computer science. For more details see http://scgp.stonybrook.edu/archives/29488This 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.