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symplectic

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symplectic [2022/09/16 15:25] – kalinin0symplectic [2022/10/12 15:07] – kalinin0
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-*2022, September 27, Tuesday, Université de Neuchâtel*+**2022, October 18, Université de Genève, salle 6-13** 
 + 
 + 
 +  Ilia Itenberg (Sorbonne) 
 +  Real enumerative invariants and their refinement 
 +  Salle 6-13, 14h15 
 + 
 +**Abstract:** 
 + 
 +The talk is devoted to several real and tropical enumerative problems. 
 +We suggest new invariants of the projective plane (and, more generally, of toric surfaces) 
 +that arise as results of an appropriate enumeration of real elliptic curves. 
 +These invariants admit a refinement (according to the quantum index) similar to the one introduced by Grigory Mikhalkin in the rational case. 
 +We discuss the combinatorics of tropical counterparts of the elliptic invariants under consideration and establish a tropical algorithm 
 +allowing one to compute them. 
 +This is a joint work with Eugenii Shustin. 
 +----------------     
 +**2022, September 27, Tuesday, Université de Neuchâtel**
  
  
Ligne 9: Ligne 26:
   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 34:
   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