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symplectic

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symplectic [2022/09/16 15:25] – kalinin0symplectic [2022/09/16 15:26] – kalinin0
Ligne 2: Ligne 2:
  
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-*2022, September 27, Tuesday, Université de Neuchâtel*+**2022, September 27, Tuesday, Université de Neuchâtel**
  
  
Ligne 9: Ligne 9:
   Room B107, 14:00   Room B107, 14:00
      
-*Abstract:*+**Abstract:**
  
 I will describe some obstructions to the existence of Lagrangian tori in subsets of Euclidean space, and also to isotopies between the tori. The obstructions come from holomorphic curves and In simple situations are sharp. As a consequence we can derive obstructions to certain 4 dimensional symplectic embeddings, which turn out not to be especially strong, but the analysis does lead to precise statements about stabilized ellipsoid embeddings. Results are taken from joint works with Emmanuel Opshtein, Jun Zhang and Kyler Siegel and Dan Cristofaro-Gardiner. I will describe some obstructions to the existence of Lagrangian tori in subsets of Euclidean space, and also to isotopies between the tori. The obstructions come from holomorphic curves and In simple situations are sharp. As a consequence we can derive obstructions to certain 4 dimensional symplectic embeddings, which turn out not to be especially strong, but the analysis does lead to precise statements about stabilized ellipsoid embeddings. Results are taken from joint works with Emmanuel Opshtein, Jun Zhang and Kyler Siegel and Dan Cristofaro-Gardiner.
Ligne 17: Ligne 17:
   Room E213, 16:00   Room E213, 16:00
  
-*Abstract:*+**Abstract:**
  
 There is an obvious family of Lagrangian tori in $S^2 \times S^2$, namely those obtained as a product of circles in the factors. We discuss the classification of such product tori up to symplectomorphisms and note that the non-monotone case is qualitatively very different from the monotone one. In the proof, we use a symmetric version of McDuff's probes. The resulting classification can be used to tackle many related questions: Which of the above tori are the image of a product torus in a ball under a Darboux embedding? What is the Hamiltonian monodromy group of the product tori? How many disjoint copies (up to Hamiltonian isotopy) of a given product torus can be packed into the ambient space? Why does the Lagrangian analogue of the flux conjecture fail so badly? If time permits we will say something about exotic tori, i.e. tori which are not symplectomorphic to product tori. This is partially based on joint work with Joontae Kim.  There is an obvious family of Lagrangian tori in $S^2 \times S^2$, namely those obtained as a product of circles in the factors. We discuss the classification of such product tori up to symplectomorphisms and note that the non-monotone case is qualitatively very different from the monotone one. In the proof, we use a symmetric version of McDuff's probes. The resulting classification can be used to tackle many related questions: Which of the above tori are the image of a product torus in a ball under a Darboux embedding? What is the Hamiltonian monodromy group of the product tori? How many disjoint copies (up to Hamiltonian isotopy) of a given product torus can be packed into the ambient space? Why does the Lagrangian analogue of the flux conjecture fail so badly? If time permits we will say something about exotic tori, i.e. tori which are not symplectomorphic to product tori. This is partially based on joint work with Joontae Kim. 
symplectic.txt · Dernière modification : 2023/11/27 17:55 de slavitya_gmail.com