WorkshopsGluing constructions of special Lagrangian and associative submanifolds
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At present we have no good general existence theory for most calibrated submanifolds, in particular for special Lagrangian submanifolds in Calabi-Yaus or associative submanifolds in manifolds with holonomy the exceptional Lie group G_2. Currently the most flexible way of constructing special Lagrangian or associative submanifolds is using gluing methods, i.e. a geometric PDE analogue of singular perturbation theory. In this talk we concentrate on our work constructing many new special Lagrangian cones using gluing techniques; time-permitting we will give an overview of our recent work constructing compact associative submanifolds in many compact G_2 manifolds and explain where the difficulties lie in both cases.
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Mark Haskins
2011-07-04
11:00:00 - 12:00:00
R101 , Astronomy and Mathematics Building
At present we have no good general existence theory for most calibrated submanifolds, in particular for special Lagrangian submanifolds in Calabi-Yaus or associative submanifolds in manifolds with holonomy the exceptional Lie group G_2. Currently the most flexible way of constructing special Lagrangian or associative submanifolds is using gluing methods, i.e. a geometric PDE analogue of singular perturbation theory. In this talk we concentrate on our work constructing many new special Lagrangian cones using gluing techniques; time-permitting we will give an overview of our recent work constructing compact associative submanifolds in many compact G_2 manifolds and explain where the difficulties lie in both cases.
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