Homological Mirror Symmetry for singularities of type T_{pqr}

Homological Mirror Symmetry for singularities of type T_{pqr}

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Ailsa Keating, Columbia University
IAS Room S-101

We present some homological mirror symmetry statements for the singularities of type $T_{p,q,r}$. Loosely, these are one level of complexity up from so-called 'simple' singularities, of types A, D and E. We will consider some symplectic invariants of the real four-dimensional Milnor fibres of these singularities, and explain how they correspond to coherent sheaves on certain blow-ups of the projective space $\P^2$, as suggested notably by Gross-Hacking-Keel. We hope to emphasize how the relations between different ``flavours" of invariants (e.g., versions of the Fukaya category) match up on both sides.