Department of Mathematics

Geometry and Topology

  •  Aleksander Doan, Columbia University
  •  Non-abelian monopoles and invariants of three-manifolds
  •  02/27/2020
  •  2:30 PM - 3:30 PM
  •  C304 Wells Hall

Floer homology groups are invariants of 3-dimensional manifolds, defined using partial differential equations of gauge theory. One version of this invariant is associated with the Yang-Mills equations and another with the Seiberg-Witten equations. While they share many similarities, it is a major open problem to find a general relation between them. I will talk about a joint project with Chris Gerig, whose goal is to relate simpler, numerical invariants obtained by taking the Euler characteristic of certain Floer homology groups. The proof, following ideas of Kronheimer and Mrowka, uses a non-abelian generalization of the Seiberg-Witten equations.

 

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Michigan State University
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