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Gauge Theory Learning Seminar

Saman Habibi Esfahani - Instanton Floer homology: real, complex, and symplectic

Saman Habibi Esfahani (Duke)

Location:  Zoom
Date & time: Friday, 29 September 2023 at 2:00PM - 3:00PM

 

Saman Habibi Esfahani

Research Assistant Professor of Mathematics

Duke University, Mathematics Department

Friday, September 29, 2023

Instanton Floer homology: real, complex, and symplectic

In 1985, Andreas Floer, by extending the methods of Morse theory and Morse homology to certain infinite-dimensional spaces, introduced novel invariants of 3-manifolds. Floer theories have been proven to be very successful tools in low-dimensional topology. Instanton Floer homology groups of a 3-manifold (M) are defined as the homology groups of a complex which is generated by the flat connections on a principal SU(2)-bundle on the 3-manifold and the differentials are defined by counting instantons on (M times mathbb{R}). In this introductory talk, we will discuss the definition and foundations of Floer theories, particularly instanton Floer homology of rational homology 3-spheres. Moreover, we will discuss (1) a complex and (2) a symplectic variation of the instanton Floer theory on 3-manifolds. 

Zoom Meeting ID: 832 798 7940
Password: 659505

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