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Explore a mathematical lecture that surveys recent developments connecting Morse theory to symplectic geometry through the lens of Weyl-type formulas. Delve into how three-manifold invariants, rooted in Morse theoretical concepts, have become central to discovering formulas analogous to Weyl's law within symplectic contexts. Learn about various symplectic Weyl laws and their mathematical significance, while examining how these theoretical frameworks apply to practical problems in dynamical systems. Discover an application to the generic density of periodic points that resolves a special case of the Closing Lemma, demonstrating the concrete implications of these abstract mathematical tools. Gain insight into the intersection of differential topology, symplectic geometry, and dynamical systems through this comprehensive mathematical exposition delivered as part of the Marston Morse 100th Anniversary celebration at the Institute for Advanced Study.
