Extra Form
일정시작 2023-10-17
일정종료 2023-10-18
배경색상 #229954
반복주기 1
반복단위 1.일(단위)
  • Date:   2023-10-17 (Tue) 16:00 ~ 17:00  

                       2023-10-18 (Wed) 16:00 ~ 17:00  

  • Place:  129-406 (SNU)   
  • Speaker:  Jun Zhang (Institute of Geometry and Physics, University of Science and Technology of China)
  • TiTle & Abstract:

New approaches to discovering symplectic non-convexity  (Oct. 17th)

In this talk, we will provide new examples of star-shaped (toric) domains in \C^2 that are dynamically convex but not symplectically convex. Our examples are based on two approaches: one is from Chaidez-Edtmair’s criterion via Ruelle invariant and systolic ratio; the other is from the ECH capacities and an analog non-linear version of Banach-Mazur distance in symplectic geometry. In particular, from the second approach, we derive the first family of examples that can be numerically verified (instead of taking a certain limit from the first approach). We will also illustrate that the information given by these two approaches is in general independent of each other. This talk is based on joint work with Dardennes, Gutt, and Ramos.


Banach-Mazur distances in symplectic and contact geometry  (Oct. 18th)

In this talk, we will discuss how the metrical geometric concept, Banach-Mazur distance, naturally fits into the study of large-scale phenomena in symplectic and contact geometry. Here, a large-scale phenomenon means a high-dimensional Euclidean space can be quasi-isometrically embedded into a space of geometric objects which include certain domains in a symplectic or contact manifold, as well as geometric structures for instance contact 1-forms. The dimension of such a Euclidean space is called the rank of a quasi-flat. Successful applications of the Banach-Mazur distance are also based on various algebraic machinery: persistence module theory, shape invariant theory, etc. The main results of this talk are establishing a general principle that almost all the spaces of geometric objects in symplectic and contact geometry admit high-rank quasi-flats. This principle can be used to distinguish geometric objects in a quantitative way. This talk is based on joint works with Vukasin Stojisavljevic and Daniel Rosen, respectively. 




List of Articles
No. Subject Author Date Views
Notice QSMS Mailing List Registration qsms 2021.09.09 12020
68 [QSMS Symplectic topology seminar-20240507]  Introduction to triangulated persistence categories qsms 2024.05.10 19
67 [QSMS Symplectic topology seminar-20230828] From Babylonian lunar observations to global surfaces of section qsms 2023.08.21 3388
66 [QSMS Symplectic topology seminar 20230817] Symplectic Torelli classes of positive entropy qsms 2023.08.14 3328
65 [QSMS Symplectic topology seminar 20230811, 0817] Spectral numbers in Tate Rabinowitz Floer Homology qsms 2023.08.04 3351
64 [QSMS Symplectic geometry seminar 2023-10-24] Linear bounds on rho-invariants and simplicial complexity of manifolds qsms 2023.10.24 3354
» [QSMS Symplectic geometry seminar 2023-10-17, 18] New approaches to discovering symplectic non-convexity / Banach-Mazur distances in symplectic and contact geometry qsms 2023.10.10 3173
62 [QSMS Seminar 2023-12-13] A user’s guide to Schubert calculus of Lagrangian Grassmannians qsms 2023.11.27 3271
61 [QSMS Seminar 2023-10-06, 11-03] Algebraic group analogues of the Slodowy slices and the structure of the set of conjugacy classes in algebraic groups / Poisson q-W-algebras qsms 2023.09.11 3385
60 [QSMS Seminar 2023-05-17] Affinizations, R-matrices and reflection functors qsms 2023.05.04 2965
59 [QSMS Seminar 20220721] Finding ALL solutions qsms 2022.07.14 3680
58 [QSMS Seminar 2022.04.19] Universal objects in vertex algebra theory qsms 2022.04.07 2981
57 [QSMS Seminar 2022.04.05] Trialities of W-algebras qsms 2022.02.15 3054
56 [QSMS Seminar 2022.03.04 (시간변경)] Introduction to Supersymmetric Field Theories qsms 2022.02.15 3301
55 [QSMS Seminar 2022-12-2] N=2 supersymmetric W algebras from Hamiltonian reduction qsms 2022.11.25 2910
54 [QSMS Seminar 2022-10-25] Rational liftings and gRSK qsms 2022.10.08 2982
53 [QSMS Seminar 2022-10-11] (q,t)-Cartan matrix and representation theories related to the specializations of the matrix file qsms 2022.09.18 2975
52 [QSMS Seminar 2022-09-27] Categories of Whittaker Modules over Lie superalgebras and Categorification of Fock Spaces qsms 2022.09.20 3012
51 [QSMS Seminar 2022-08-31] Localization of the category of modules over quiver Hecke algebras qsms 2022.08.25 3096
50 [QSMS Seminar 2022-08-24] Vector bundles and representation theory on a curve qsms 2022.08.13 3050
49 [QSMS Seminar 2021.10.26, 10.28] Feigin-Semikhatov duality in W-superalgebras qsms 2021.10.13 3139
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