We present some homological mirror symmetry statements for the singularities of type Tp,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 4-dimensional Milnor fibres of these singularities, and explain how they correspond to coherent sheaves on certain blow-ups of the projective space P2, 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.
This video is part of the Institute for Advanced Study‘s Symplectic geometry seminar.
