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Explore advanced concepts in symplectic geometry through this joint IAS/PU Symplectic Geometry Seminar lecture. Delve into the homotopy rigidity properties of nearby Lagrangian cocores, focusing on exact Lagrangian submanifolds in cotangent bundles that coincide with cotangent fibers outside compact sets while remaining disjoint from at least one cotangent fiber. Learn about groundbreaking research demonstrating that any nearby Lagrangian fiber in T∗ℂℙ² or T∗(Sⁿ⁻ᵏ×ℝᵏ) is smoothly isotopic to a cotangent fiber relative to the boundary in the complement of the missed fiber. Discover how these specific results emerge from broader homotopy rigidity theorems concerning exact Lagrangian fillings of unknots in subcritical Weinstein manifolds, representing collaborative work with Yash Deshmukh and Alex Pieloch that advances our understanding of the geometric and topological constraints governing Lagrangian submanifolds in symplectic topology.
