Title: Special Lagrangians with Cylindrical Tangent Cones
Abstract: What does a tangent cone see—and what does it miss? I will discuss this question for singular special Lagrangian submanifolds with cylindrical tangent cones. The main result is the construction of new special Lagrangians $Y\subset \C^{n+1}, n\geq 3$, defined near the origin, such that $Y$ has an isolated singularity, while its tangent cone is $C\times\R$, whose singular set is non-isolated. Thus the singular set of the tangent cone can be strictly larger than that of the submanifold it models. Such examples arise, in particular, when $C$ is a suitable pair of transverse planes. A necessary feature of this construction is that the link of $C$ is disconnected. I will also discuss ongoing work suggesting a complementary rigidity phenomenon: when $C$ has a smooth connected link and satisfies certain spectral properties, such isolated singularities should not occur.
Gabor Szekelyhidi
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