Gökova Geometry Topology Institute

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===== Research Session on Amoebas and Symplectic Geometry =====
=====(Sep 29-Oct 8, 2022) =====

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The session will bring together leading experts on amoebas of algebraic curves to discuss the very recent applications of amoebas in symplectic geometry, and to brainstorm eventual further applications in this direction. The focus will be made on the tropical limit of amoebas, and the way it appears in the symplectic framework. The session will include ample informal discussions as well as some talks reviewing the state-of-the-art technique needed for these applications.

This event will be held in person at Hotel Yucelen. 

=== List of Participants ===

|Alexander Bobenko (TU-BERLIN)|Tobias Ekholm  (UU-UPPSALA) |
|Sergey Finashin (METU)   |Ilia Itenberg (IMJ-PRG)  |   
|Grigory Mikhalkin (UNIGE) |Georgios Dimitroglu-Rizell  (UU-UPPSALA)  |
          

**Organizing Committee**: [[sfinashin@gmail.com|Sergey Finashin]] [[g.m@cern.ch|Grigory Mikhalkin]][[ilia.itenberg@imj-prg.fr|Ilia Itenberg]] and [[eylem.yildiz@duke.edu|Eylem Zeliha Yıldız]].

 
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=== Summary Report ===

The session served as a place for exchanging ideas among the participants. Various themes motivated by the use of real and complex curves as well as their amoebas in the framework of symplectic geometry were discussed. This included the problem of rigid isotopy of real affine cubic surfaces, implications of the adjunction inequality for complex smooth surfaces, the shape of soliton limits of generalized amoebas of simple Harnack curves, "bulky" phenomenon for Lagrangian isotopies in narrow spaces, as well as a discussion of refined enumerative invariants in the context of skein relations from the knot theory.

Gökova Geometry Topology Institute

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