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Explore the intersection of Hodge theory and representation theory of real reductive groups in this arithmetic geometry seminar from the Institute for Advanced Study. Survey the progress made on Wilfried Schmid and Kari Vilonen's 2011 proposal to use natural Hodge structures from geometry to solve challenging problems in representation theory of real groups. Examine specific areas where Hodge structures play crucial roles, including Vogan's theory of lowest K-types, unitarity questions, and the Orbit Method. Learn about the techniques that make this theoretical framework practical and discover how geometric methods can illuminate representation-theoretic problems. The presentation draws from collaborative research with Kari Vilonen and Lucas Mason-Brown, offering insights into current developments in this active area of mathematical research.
