===== Research Session on Tropical and Symplectic Geometry =====
=====(Oct 1-Oct 11, 2024) =====

{{:events:2024:24rstropicalsymplectic.jpg|}}

This event will be held in person at Hotel Yucelen.  


=== Confirmed Participants ===

|Selman Akbulut (GGTI)|Alexei Borodin (MIT) |Alexander Bobenko (TU Berlin) |
|Weimin Chen (UMass)|Georgios Dimitroglou Rizell (Uppsala U)|Tobias Ekholm (Uppsala U)|
|Sergey Finashin (METU) |Ilia Itenberg (Sorbonne U) | Grigory Mikhalkin (Geneva U)| 
|Stepan Orevkov (IMT UPS) |Cem Yalım Özel (Boğaziçi U) | Felix Schlenk (U of Neuchâtel) |
|Mikhail Shkolnikov (IMI BAS) |Umut Varolgunes (Koç U)  |Eylem Z Yıldız (GGTI)|


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


=== List of Talks ===
^Speaker    ^ Title ^
|Alexander Bobenko| Uniformization of M-curves.|
|Alexei Borodin | Tropical geometry of dimer models.|
|Georgios Dimitroglou Rizell| An attempt to prove the instability of Markov tori.|
|Tobias Ekholm|Skein valued curve counts, recursion relations, and D-modules.|
|Stepan Orevkov| Algebraically unrealizable complex orientations of real pseudoholomorphic curves.|
|Felix Schlenk| Barriers in symplectic geometry.|
|Mikhail Shkolnikov| Quadratic forms and tropical caustics.|
|Umut Varolgunes|Higher genus structures in symplectic cohomologies|

===Summary Report===

Eight main talks were distributed during the workshop, followed by discussion sessions.  

During the discussions, we identified the following question. Hind-Mikhalkin-Schlenk have shown that a monotone Markov Lagrangian torus in the projective plane has precisely three symplectic spheres in its complement up to Hamiltonian isotopy. In the same time, non-monotone tori can have more than 3 symplectic spheres in their complement. This turns our attention to the wall-crossing formula for the homology classes of the three spheres. There are applications to the understanding of the Hamiltonian isotopy class of a torus after inflating some given symplectic sphere in its complement.