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Explore the underlying geometry behind the analytic invariants of singular foliations by curves in (C^2,0) in this 49-minute conference talk delivered by Laura Ortiz Bobadilla from UNAM. Delve into advanced mathematical concepts at the intersection of foliations, complex geometry, and Painlevé equations as part of a special event celebrating the 60th birthday of Frank Loray. Examine the intricate relationships between geometric structures and analytic properties in complex analysis, focusing specifically on how singular foliations behave in two-dimensional complex spaces. Learn about the mathematical frameworks that connect foliation theory with complex geometric analysis, and discover how these concepts relate to the broader field of Painlevé equations. Gain insights from cutting-edge research presented at the Instituto de Matemática Pura e Aplicada, featuring contributions from an international scientific committee including experts from IMPA, Université de Montreal, Université de Rennes, Universidad de Valladolid, and Kobe University.
