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In this Mathematics Department Colloquium talk, explore Daniel Pomerleano's research on cohomological splittings in algebraic and symplectic geometry. Beginning with a review of fundamental results established by Atiyah, Bott, and Kirwan in the 1980s regarding rational cohomology of compact symplectic manifolds with Hamiltonian actions of connected, compact groups, the lecture then advances to discuss recent integral and stable homotopical refinements. Discover how these new developments incorporate concepts from chromatic homotopy theory and Gromov-Witten theory, based on Pomerleano's joint work with Shaoyun Bai, Guangbo Xu, and Constantin Teleman. This April 4, 2025 presentation from UMass Boston's Daniel Pomerleano at Stony Brook Mathematics offers valuable insights for those interested in advanced mathematical concepts at the intersection of algebraic and symplectic geometry.
