Berlin-Hamburg-Seminar am 26.6.2017

Vsevolod Shevchishin (Olsztyn) On symplectic mapping class group of rational 4-manifolds: Presentation in the cases D_l and E₅

The symplectic mapping class group Symp(X,ω) is the group of symplectomorphisms of (X,ω) modulo symplectic isotopies. It appears that Symp(X,ω) depends not only on the manifold X, but also on the symplectic form. In my talk I describe two special types of symplectic forms on rational 4-manifold (l-fold blow-ups of CP²), called D_l and E_l. For symplectic forms of those types I describe a construction which allows to find a natural geometric presentation of the group Symp(X,ω), and make a calculation for the types D_l and E₅.

Kyler Siegel (MIT) Subflexible symplectic manifolds and deformed symplectic invariants

One school of symplectic geometers believes that every symplectic creature either (a) satisfies an h principle or (b) has some nontrivial pseudoholomorphic curve invariant. Recent years have considerably progressed our understanding of the objects constituting category (a). In this talk, I will construct a class of examples, called "subflexible", which lie surprisingly close to the interface between (a) and (b). I will explain what types of symplectic invariants one must use to properly understand these examples and place them in category (b). Time permitting, I will end with some speculations about future symplectic invariants and exotica.