Differential Geometry and Topology

course: Special Lagrangian cones over odd genus surfaces by gluing

speaker: Mark Haskins (Imperial College)

abstract: We describe recent joint work with Nikos Kapouleas which constructs a countably infinite family of special Lagrangian (SLG) cones over any compact orientable surface of odd genus. These are the first examples of SLG cones whose links are surfaces of genus greater than 1. The construction uses a geometric PDE gluing method. In this talk I will explain what this means, describe briefly analogous previous constructions and outline the basic approach taken.

I will describe the basic building blocks and set up of our construction, outline the steps needed in the proof and point out where the technical difficulties lie. Some discussion about how we overcome these difficulties will be given.

Gluing References:

1. 'Constructions of minimal surfaces by gluing minimal immersions', N. Kapouleas, Clay Mathematics Proceedings. (Survey article) 2. 'Complete constant mean-curvature surfaces in Euclidean three-space', N. Kapouleas, Annals of Maths, 131 (1990), 239-330. 3. 'Constant mean curvature surfaces constructed by fusing Wente tori', N. Kapouleas, Invent. math. 119 (1995), 443-518.

SLG cones and singularities:

1. 'Constructing Special Lagrangian cones', M. Haskins, University of Texas dissertation, 2000. 2. 'Special Lagrangian cones', M. Haskins, American Journal of Maths, 126 (2004), 845-871. 3. 'Special Lagrangian submanifolds with isolated conical singularities. V. Survey and applications', D. Joyce, J. of Differential Geometry, 63 (2003), 279-347. 4. 'Special Lagrangian cones with higher genus links', M. Haskins and N. Kapouleas, in preparation.

timetable:
Tue 14 Sep, 11:15 - 12:15, Sala Conferenze Centro De Giorgi
Mon 20 Sep, 18:15 - 19:15, Sala Conferenze Centro De Giorgi
Tue 21 Sep, 17:00 - 18:15, Sala Conferenze Centro De Giorgi
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