?

Shortcut

PrevPrev Article

NextNext Article

Larger Font Smaller Font Up Down Go comment Print
?

Shortcut

PrevPrev Article

NextNext Article

Larger Font Smaller Font Up Down Go comment Print
Extra Form
일정시작 2022-05-12
일정종료 2022-05-12
배경색상 #7164D0
  • Date :  2022-05-12  14:00 ~ 16:00  
  • Place :  129-406 (SNU)   or   Zoom
  • Speaker :  Yat-Hin Suen  (IBS-CGP)

  • TiTle  : Tropical Lagrangian multi-sections and tropical locally free sheaves

  • Abstract : Based on the SYZ conjecture, it is a folklore that "mirror of Lagrangian multi-sections are locally free sheaves". However, due to the non-trivial contribution of holomorphic disks and wall-crossing phenomenon, this folklore has only been verified in very few cases. In this talk, I would like to introduce the notion of tropical Lagrangian multi-sections over any integral affine manifold with singularities $B$ equipped with a polyhedral decomposition $\mathscr{P}$. As the name suggests, tropical Lagrangian multi-sections are tropical/combinatorial replacement of Lagrangian multi-sections in the SYZ program. Given a tropical Lagrangian multi-section, together with some linear algebra data, we are going to construct a locally free sheaf $\mathcal{E}_0(\mathbb{L})$ on the log Calabi-Yau space $X_0(B,\mathscr{P})$ associated to $(B,\mathscr{P})$, which plays a key role in the famous Gross-Siebert program. The locally free sheaves arise as such construction are not arbitrary and we call them tropical locally free sheaves. I will also provide the reverse construction and establish a correspondence between isomorphism classes of tropical locally free sheaves and tropical Lagrangian multi-sections modulo certain non-trivial equivalence. I will also provide a combinatorial criterion for the smoothability of the pair $(X_0(B,\mathscr{P}),\mathcal{E}_0(\mathbb{L}))$ in dimension 2 under some additional assumptions on $\mathscr{P}$ and $\mathbb{L}$. Finally, if time permits, I will discuss how to prove homological mirror symmetry between Lagrangian multi-sections and locally free shaves using microlocal sheaf theory.

     

     

     


List of Articles
No. Subject Author Date Views
Notice QSMS Mailing List Registration qsms 2021.09.09 12035
28 [QSMS Monthly Seminar] Closed orbits and Beatty sequences qsms 2021.06.24 3750
27 [QSMS Monthly Seminar] Canonical basis qsms 2020.11.18 9217
26 [QSMS Monthly Seminar] A survey on symplectic fillings and Milnor fibers of a normal complex surface singularity qsms 2021.03.26 3774
25 [QSMS Monthly Seminar] The dimension of the kernel of an Eisenstein ideal qsms 2022.03.25 3042
24 [QSMS Monthly Seminar] Quiver Hecke algebras and open Richardson varieties qsms 2023.09.22 3122
23 [QSMS Monthly Seminar 2024-04-12] Local systems and finite group symmetry in Floer theory / Calabi-Yau structures on Rabinowitz Fukaya categories qsms 2024.04.12 154
22 [QSMS Monthly Seminar 2024-03-22] Lifting problem for universal quadratic forms / Poincare duality in Rabinowitz Floer homology qsms 2024.03.22 2387
21 [QSMS Monthly Seminar 2023-12-14] Simple singularity and their friends qsms 2023.12.14 2881
20 [QSMS Monthly Seminar 2023-11-11] Cluster structures on polygon spaces / From classical to quantum integrability qsms 2023.11.10 3258
19 [QSMS Monthly Seminar 2023-10-13] Quantum Grothendieck rings of Hernandez-Leclerc categories / Regular Schur labeled skew shape posets and their 0-Hecke modules qsms 2023.10.13 3059
18 [QSMS Monthly Seminar 2023-05-26] Lagrangian submanifolds and their Legendrian lifts qsms 2023.05.26 3100
17 [QSMS Monthly Seminar 2023-04-21] Lagrangian submanifolds and their Legendrian lifts qsms 2023.04.21 3038
16 [QSMS Monthly Seminar 2023-03-24] Rational points on abelian varieties qsms 2023.03.24 2981
15 [QSMS Monthly Seminar 2022-12-02] Extended crystal structures of Hernandez-Leclerc categories qsms 2022.12.02 3045
14 [QSMS Monthly Seminar 2022-10-28] Oscillator representations of quantum affine algebras   qsms 2022.10.30 3011
13 [QSMS Monthly Seminar 2022-09-30] Monotone Lagrangians via toric degenerations: algebraic approach qsms 2022.09.30 3047
12 [QSMS Mini-course] Pablo Portilla cuadrado (University of Lille) qsms 2022.07.04 3106
11 [QSMS Geometry seminar 2023-05-25] Symplectic field theory and codimension-2 stable Hamiltonian submanifolds qsms 2023.05.25 3007
10 [QSMS Geometry Seminar 20221230] Morphism spaces between coisotropic A-branes qsms 2022.12.27 2987
9 [QSMS Geometry Seminar 2022-05-17, 19] Symplectic Criteria on Stratified Uniruledness of Affine Varieties and Applications qsms 2022.05.09 3110
Board Pagination Prev 1 2 3 4 5 6 7 8 Next
/ 8