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Geometric Analysis Seminar

Atiyah-Floer Conjecture and Mixed Equation

Aliakbar Daemi (Simons Center for Geometry and Physics)

Location:  Hill 705
Date & time: Friday, 30 March 2018 at 2:45PM - 3:45PM

Abstract: In 1980's, Floer introduced two remarkable invariants in 3-manifold topology and Symplectic geometry, which are known as instanton Floer homology and Lagrangian Floer homology.  The Atiyah-Floer conjecture states that these two invariants are related to each other. In my talk, I will introduce the mixed equations and show how they are useful to study the relationship between instanton Floer homology and Lagrangian Floer homology. In particular, mixed equations can be used to prove some versions of the Atiyah-Floer conjecture, generalizing earlier work of Dostoglou and Salamon. In this talk, I will focus on analytical aspects of the mixed equation.

This is a joint work with Kenji Fukaya and Max Lipyanskyi.

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