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trResearch Session on Tropical and Symplectic Geometry
(Oct 1-Oct 11, 2024)
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: Sergey Finashin Ilia Itenberg Grigory Mikhalkin and 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.
