What is the mirror to a Weinstein Neighborhood? (Jeffrey Hicks, Edinburgh)

06.12.2024 14:00 – 16:00

Abstract:
A fundamental result in symplectic geometry is that every Lagrangian
submanifold has a small standard neighborhood. The existence of this
Weinstein Neighborhood implies that there are no “local” invariants of a
Lagrangian submanifold other than the topology of the Lagrangian
submanifold. Mirror symmetry is a conjectured dictionary between
symplectic and algebraic geometry on a pair of mirror spaces. Under this
dictionary, Lagrangian submanifolds in a symplectic manifold are related
to sheaves on the mirror algebraic space.

In this talk — which will only use intuition, not techniques from
symplectic geometry — we give a candidate definition of the “Weinstein
neighborhood” of a sheaf on an algebraic space, which extends the
definition of an affine neighborhood of a point. We'll prove the
existence of such a neighborhood for the structure sheaf of a hyperplane
in projective space. Time permitting, we'll draw connections to tropical
geometry and spaces of nonpositive curvature.

Lieu

Bâtiment: Conseil Général 7-9

Room 6-13, "Geneva-Neuchatel Symplectic Geometry Seminar" GeNeSys (joint seminar with the Université de Neuchâtel)

entrée libre