?

단축키

Prev이전 문서

Next다음 문서

크게 작게 위로 아래로 댓글로 가기 인쇄
?

단축키

Prev이전 문서

Next다음 문서

크게 작게 위로 아래로 댓글로 가기 인쇄
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
번호 제목 글쓴이 날짜 조회 수
공지 QSMS Mailing List Registration qsms 2021.09.09 2461
82 [QSMS-BK21 Toric Geometry Seminar] Moduli Space of Special Lagrangians in the Complement of an Anticanonical Divisor qsms 2022.04.12 978
81 [SNU Number Theory Seminar 2022-05-06] On an upper bound of the average analytic rank of a family of elliptic curves qsms 2022.04.19 966
80 [SNU Number Theory Seminar 20220401] Randomness and structure for sums of cubes qsms 2022.03.28 954
79 [QSMS Geometry Seminar 2022-05-17, 19] Symplectic Criteria on Stratified Uniruledness of Affine Varieties and Applications qsms 2022.05.09 927
78 [QSMS Monthly Seminar] Introduction to finite-dimensional representations of quantum affine algebras qsms 2021.12.03 921
77 [QSMS Seminar 2022.04.19] Universal objects in vertex algebra theory qsms 2022.04.07 920
76 [QSMS Seminar 2022.04.05] Trialities of W-algebras qsms 2022.02.15 917
75 [Seminar 2020.12.10] Zeta함수와 L함수에 대한 역사적 고찰III qsms 2020.12.08 907
74 [Seminar 2021.01.07] Zeta함수와 L함수에 대한 역사적 고찰VII qsms 2021.01.04 898
73 [SNU Number Theory Seminar 2022-05-13] A singular function containing all Lagrange numbers less than three qsms 2022.04.12 890
72 [QSMS Monthly Seminar] Yokonuma Hecke algebras and invariants of framed links qsms 2022.05.27 874
71 [SNU Number Theory Seminar 2022-08-08] Geometry of the $B_{dR}^+$-Grassmannian qsms 2022.08.04 867
70 [QSMS Mini-course] Pablo Portilla cuadrado (University of Lille) qsms 2022.07.04 858
69 [SNU Number Theory Seminar 2022-08-11] The dual Lagrangian fibration of hyper-Kähler manifolds qsms 2022.08.04 851
68 [Seminar 2020.12.17] Zeta함수와 L함수에 대한 역사적 고찰IV qsms 2020.12.08 845
67 [SNU Number Theory Seminar 2022-06-21] Arithmetic local systems over the moduli space of curves qsms 2022.07.21 840
66 [QSMS Seminar 2022-08-24] Vector bundles and representation theory on a curve qsms 2022.08.13 835
65 [QSMS Seminar 2022-08-31] Localization of the category of modules over quiver Hecke algebras qsms 2022.08.25 834
» [QSMS Geometry Seminar 2022-05-12] Tropical Lagrangian multi-sections and tropical locally free sheaves qsms 2022.05.07 834
63 [QSMS Monthly Seminar] The dimension of the kernel of an Eisenstein ideal qsms 2022.03.25 834
Board Pagination Prev 1 2 3 4 5 6 7 8 Next
/ 8