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One of the tried-and-true techniques in representation theory is to apply topological invariants to spaces built out of Lie groups. The workshop will study this paradigm where the invariant is equivariant elliptic cohomology. Elliptic cohomology has deep roots in homotopy theory, algebraic geometry, and mathematical physics. The resulting interplay has proven to be fertile territory, rich with intricate examples in many disciplines, including integrable systems, enumerative geometry, and elliptic algebras. The recent and ongoing understanding of the geometry of elliptic cohomology has revealed new conceptual understanding and computational tools. The focus of this workshop will be to apply these new Ideas to geometric representation theory. An ideal participant will have experience in one of the related areas, but need not have exposure to all of them. In particular, prior expertise in elliptic cohomology is not necessary. We look forward to bringing together advanced graduate students and postdocs from a mix of backgrounds for a workshop centered on cross-disciplinary interaction and collaboration.