Mathematics Colloquia and Seminars

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Symplectic manifolds decompose into a symplectic divisor and an exact Weinstein manifold. We will discuss both sides of this essential decomposition. On the divisor side, we will focus on symplectic surfaces in 4-manifolds, particularly the longstanding symplectic isotopy problem. We will leverage singularities and study symplectic versions of line arrangements and rational cuspidal curves. On the Weinstein side, we will see how to encode the symplectic geometry of a 2n-dimensional manifold using the topology of an n-dimensional singular complex: the Lagrangian skeleton.