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Award ID contains: 1942363

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  1. ; (, Selecta Mathematica)
    Abstract This article introduces a new method to construct volume-filling symplectic embeddings of 4-dimensional ellipsoids by employing polytope mutations in toric and almost toric varieties. The construction uniformly recovers the full sequences for the Fibonacci Staircase of McDuff–Schlenk, the Pell Staircase of Frenkel–Müller and the Cristofaro-Gardiner–Kleinman Staircase, and adds new infinite sequences of ellipsoid embeddings. In addition, we initiate the study of symplectic-tropical curves for almost toric fibrations and emphasize the connection to quiver combinatorics. 
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  2. (, Journal of Fixed Point Theory and Applications)
    Abstract We construct closed arboreal Lagrangian skeleta associated to links of isolated plane curve singularities. This yields closed Lagrangian skeleta for Weinstein pairs $$(\mathbb {C}^2,\Lambda )$$ ( C 2 , Λ ) and Weinstein 4-manifolds $$W(\Lambda )$$ W ( Λ ) associated to max-tb Legendrian representatives of algebraic links $$\Lambda \subseteq (\mathbb {S}^3,\xi _\text {st})$$ Λ ⊆ ( S 3 , ξ st ) . We provide computations of Legendrian and Weinstein invariants, and discuss the contact topological nature of the Fomin–Pylyavskyy–Shustin–Thurston cluster algebra associated to a singularity. Finally, we present a conjectural ADE-classification for Lagrangian fillings of certain Legendrian links and list some related problems. 
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  3. ; (, Annals of Mathematics)
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  4. ; ; (, Geometry & Topology)
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