Lecture Series by Visiting Kalman Fellow

Francesco Lin (Columbia University)

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Overview


Monopole Floer homology is a package of subtle invariants of three-manifolds arising from the study of the Seiberg-Witten equations. In this lecture series, we will discuss its properties, construction, and applications. 

Programme


  • Lecture 1: Formal properties and topological applications  (10am -11am, 24 August, in 303-257)

  • Lecture 2: S^1-equivariant Morse theory   (11am -12pm, 24 August, in 303-257)

  • Lecture 3: The Seiberg-Witten equations  (10am -11am, 25 August, in 260-325)

  • Lecture 4: Computations of the invariants   (11am -12pm, 25 August, in 260-325)

Colloquium


Title: Homology cobordism and the geometry of hyperbolic three-manifolds   (4-5pm, 24 August, in 303-MLT1)

Topology in four dimensions has very unique features, and an object that perfectly exemplifies them is the three-dimensional homology cobordism group. After introducing it and discussing its significance and challenges, I will focus on interactions with Thurston’s geometrization program, and discuss some results aimed at understanding the relation between hyperbolic geometry and homology cobordism.