BRANDEIS, HARVARD, MIT, NORTHEASTERN JOINT COLLOQUIUM AT HARVARD: | Paul HackingUniversity of Massachusetts, Amherst |
Mirror Symmetry and Fano manifolds |

on Thursday, April 26, 2018, at Tea at 4 pm, Talk at 4:30 pm in Science Center Hall A | ||

Roughly speaking, a Fano manifold is a complex manifold with positive Ricci curvature. The Riemann sphere is the unique Fano manifold in complex dimension 1, there are 10 topological types in dimension 2, and 105 in dimension 3. I will describe a project initiated by Coates, Corti, Galkin, Golyshev, and Kasprzyk to classify Fano manifolds using mirror symmetry. This is joint work with Alessio Corti, Mark Gross, and Andrea Petracci. |

CMSA SPECIAL SEMINAR ON SYMPLECTIC GEOMETRY: | Weiwei WuUniversity of Georgia |
Lagrangian surgery formulae and applications |

on Monday, April 30, 2018, at 1:30 - 2:30 pm in CMSA Building, 20 Garden Street, Room G10 | ||

I will explain two new proofs of Lagrangian surgery formulae in Lagrangian Floer theory. The first one deals with transversal intersections and is robust with respect to auxiliary data near the transversal intersection. Our main innovation is to count the holomorphic solution in a local problem similar to FOOO's original proof using Lefschetz fibration, which simplifies the problem. For Lagrangian surgery with general clean intersections, we prove a new compactness theorem for holomorphic curves with degenerate Lagrangian boundary. This compactness result potentially has applications to problems of understanding the behavior of holomorphic disks with other types of Lagrangian degenerations. This is a joint work with Cheuk-Yu Mak. |