Mathematics Colloquia and Seminars

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A Weinstein manifold is an open symplectic manifold equipped with a good expanding vector field. Building on work by Nadler, Starkston showed that in dimensions 2 and 4 every Weinstein manifold can be "arborealized" to one whose skeleton has only combinatorially-prescribed singularities. For surfaces, these skeleta are trivalent graphs, which suggests a diagramatic calculus for constructing invariants. In my talk I will discuss a new such construction, which from a trivalent graph produces a diagram of (Z/2-graded) dg-categories, with the resulting homotopy limit being invariant under Weinstein homotopy. After constructing some tools in the homotopy theory of model categories, we will define these diagrams explicitly and give a proof of invariance which was just discovered last week!