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Explore advanced topics in symplectic topology and gauge theory through this comprehensive lecture series from the Jean-Morlet Chair semester program. Delve into the fundamental connections between moduli spaces, geometric objects, and minimality problems that appear across modern geometry, from Perelman's proof of the Poincaré conjecture using Ricci flow to Taubes' spectacular proof of the Weinstein conjecture. Examine how Floer theory pervades symplectic topology and its extraordinary applications in low-dimensional differential topology, while investigating J-holomorphic curves as the core of Gromov-Witten theory and their applications in almost complex geometry. Study cutting-edge research including the Fukaya category's role in counting curves, Floer theory of cotangent bundles and string topology, Liouville structures on cobordisms, the degenerate special Lagrangian equation, and virtual fundamental cycles in contact homology. Learn from leading experts as they present recent developments in symplectic and differential topology, covering topics that represent the current frontier of research as evidenced by their prominence in recent International Congress of Mathematicians plenary talks.
