Explore a lecture on unitary representations of reductive Lie groups, presented by Harvard's Wilfried Schmid at the University of Miami. Delve into a conjecture and recent progress in this field, utilizing Hodge theory. Gain insights into the collaborative work with Kari Vilonen as the speaker covers topics such as classification schemes, regular polynomics, High Chandra's Theorem, vanishing theorems, Logan's Algorithm, intersection theory, and the vanishing conjecture. Enhance your understanding of advanced mathematical concepts in this 48-minute presentation, which also addresses additional questions in the field.