This semester we are learning almostToric Fibrations.
The notes are here: Notes
Zoom link: https://umn.zoom.us/j/94798206643
Time: Thursday 9-11AM
The tentative schedules is as followes:
9.15: Overview by Jie Min
9.22: Basics of toric and integral affine structures (Yi Du). [Evans 1,2,3,6,7]. [Symington 1,2,3,4,5]
9.29: Delzant construction (Yi Du)
10.6: Operations compatible with ATF structures (Jie Min). [Evans 8,9],[Symington 6,10]
10.13: Visible surfaces (Shuo Zhang). [Evans 9,10,11],[Symington 9,10]
10.20: Vianna's exotic lagrangians (Shuo Zhang). [Vianna 1],[Vianna 2], [Vianna 3]
10.27: Symplectic embeddings (Shengzhen Ning). [Casals-Vianna], [Shelukhin-Tonkonog-Vianna], [Gardiner-Holm-Mandini-Pires]
11.3: Tropical curves. (Ke Zhu).[Mikhalkin 1],[Mikhalkin 2],[Casals-Vianna],
11.10: Symplectomorphisms of Mirrors to LCY surfaces (Jie Min) [Hacking-Keating], [Bernard, Matessi, Solomon]
11.17:Break
11.24:Break
12.1: Wall crossing formula. Distinguishing exotic Lagrangians by count of Maslov 2 discs (Shuo Zhang)
12.8: Tropical to Lagrangian correspondance (Jie Min)
References:
[Evans]: Lectures on Lagrangian torus fibrations by Johny Evans
[Symington]: Four dimensions from two in symplectic topology by Margaret Symington
[Vianna 1]: On exotic Lagrangian tori in CP^2
[Vianna 2]: Infinitely many exotic monotone Lagrangian tori in CP^2
[Vianna 3]: Infinitely many monotone Lagrangian tori in del Pezzo surfaces
[Casals-Vianna]: Full Ellipsoid Embeddings and Toric Mutations
[Shelukhin-Tonkonog-Vianna] Geometry of symplectic flux and Lagrangian torus fibrations
[Gardiner-Holm-Mandini-Pires] On infinite staircases in toric symplectic four-manifold
[Sackel-Song-Varolgunes-Zhu] On certain quantifications of Gromov's non-squeezing theorem.
[Mikhalkin 1]: Examples of tropical-to-Lagrangian correspondence
[Mikhalkin 2]: Enumerative tropical algebraic geometry in R^2
[Hacking-Keating]: Homological mirror symmetry for log Calabi-Yau surfaces:
[Bernard, Matessi, Solomon]: Symmetries of Lagrangian fibrations