This is a series seminar organized by MCM on Symplectic Geometry and Mathematical Physics at MCM410 on each Wednesday. If you have any questions, please feel free to contact us (mcmoffice@math.ac.cn).
Yalong Cao and Zhengyi Zhou
Each Wednesday, MCM410
Upcoming talks:
Date: June 26, 2024
Time: 14:00-15:00
Speaker: Dr. Yu Pan (Tianjin University)
Title: Augmentations and Exact Lagrangian surfaces
Abstract: Exact Lagrangian surfaces are important objects in the derived Fukaya category. Augmentations are objects of the augmentation category, which is the contact analog of the Fukaya category. In this talk, we discuss various relations between augmentations and exact Lagrangian surfaces. In particular, we realize augmentations, which is an algebraic object, fully geometrically via exact Lagrangian surfaces.
Date: April 10, 2024
Time: 10:30-11:30
Speaker: Prof. Si Li (Tsinghua Univ)
Title: Holomorphic Chern-Simons at Large N
Abstract: We describe the coupling of holomorphic Chern-Simons theory at large N with Kodaira- Spencer gravity. The 1st order deformation is realized by the Loday-Quillen-Tsygan Theorem on the Lie algebra cohomology of large N matrices. We show that the dynamics of Kodaira-Spencer gravity is fully recovered from this large N holomorphic Chern-Simons theory.
Date: May 15, 2024
Time: 10:00-11:00
Speaker: Prof. Zhengyu Zong (Tsinghua Univ)
Title: Open WDVV equations for toric Calabi-Yau 3-folds
Abstract: The Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations is an important system of equations in the study of genus zero Gromov-Witten invariants. It implies the associativity of the quantum product. The associativity of the quantum product has many important applications including the recursive formula given by Kontsevich and Manin that calculates the Gromov-Witten invariants of the projective plane. The system of open WDVV equations plays an important role in the study of open Gromov-Witten invariants. It can be viewed as an extension of the WDVV equation to the open sector. The natural structure that captures the WDVV equation is that of a Frobenius manifold. Similarly, the system of open WDVV equations determines the structure of an F-manifold, a generalization of a Frobenius manifold.
In this talk, we prove two versions of open WDVV equations for toric Calabi-Yau 3-folds. The first version leads to the construction of a semi-simple (formal) Frobenius manifold and the second version leads to the construction of a (formal) F-manifold. This is a joint work with Song Yu.
Date: May 29, 2024
Time: 10:30-11:30
Speaker: Prof. Bohan Fang (Beijing International Center for Mathematical Research)
Title: Oscillatory integrals in mirror symmetry
Abstract: I will describe the oscillatory and period integrals on the B-side of mirror symmetry. They correspond to Gromov-Witten primary and descendant invariants of Gamma-modified twisted Chern classes of the mirror coherent sheaves. The cycles for integration correspond to these mirror sheaves by homological mirror symmetry, and one may obtain higher genus invariants if using correct higher genus B-model integrands. I will explain some examples in the setting of toric mirrors and Gross-Hacking-Keel mirror LG models, and discuss application to Gamma conjectures in the toric setting.
Date: May 29, 2024 (Wednesday)
Time: 16:30-17:30
Speaker: Prof. Qizheng Yin (Beijing International Center for Mathematical Research)
Title: Cohomological and motivic aspects of compactified Jacobian fibrations
Abstract: Beauville showed using Fourier transforms that the Chow ring/motive of an abelian variety admits a natural, multiplicative decomposition. I will explain how Beauville’s theory can be extended to certain abelian fibrations with singular fibers. One notable consequence of this extension is a proof of the P=W conjecture in nonabelian Hodge theory. In this talk I will focus on aspects beyond P=W, and discuss some related open questions. Joint work in progress with Davesh Maulik and Junliang Shen.
Date: May 31, 2024 (Friday)
Time: 14:00-15:00
Speaker: Dr. Oliver Edtmair (University of California, Berkeley)
Title: Systoles of convex energy hypersurfaces
Abstract: Hofer-Wysocki-Zehnder proved that every strictly convex energy hypersurface in R^4 possesses a disk-like global surface of section. They asked whether a systole, i.e. a periodic orbit of least action, must span such a disk-like global surface of section. In my talk, I will give an affirmative answer to this question, based on joint work in progress with Abbondandolo and Kang. I will explain how this result can be used to obtain a sharp symplectic embedding result for convex domains in R^4. Moreover, I will explain how this relates to the strong Viberbo conjecture on the equivalence of normalized symplectic capacities.
Date: June 12, 2024
Time: 14:00-15:00
Speaker: Dr. Yu-Wei Fan (YMSC)
Title: Finite subgroups of derived automorphisms of general K3 surfaces
Abstract: We will discuss a classification of finite subgroups of the group of autoequivalences of the derived category of coherent sheaves on a general K3 surface. The main tool is the examination of the actions of autoequivalences on the space of Bridgeland stability conditions, which will be explained in the talk, along with related background on mirror symmetry. Joint work with Kuan-Wen Lai.
Date: June 19, 2024
Time: 14:00-15:00
Speaker: Dr. Honghao Gao (YMSC)
Title: Legendrian knots and Lagrangian fillings
Abstract: Legendrian knots and their exact Lagrangian fillings are central objects to study in low dimensional contact and symplectic topology. Therefore, it is an important question to classify exact Lagrangian fillings up to Hamiltonian isotopy. It is conjectured that this classification is controlled by a quiver and some derived algebraic structures. In this talk, I will review the historical developments, and explain the algebraic machinery to distinguish fillings. Then, I will discuss the ideas to obtain a subjectivity result, which involving new ideas such as understanding polygons on surfaces, quiver with potentials, etc. This is based on a joint work with Roger Casals.
