Geometry and Physics Seminar
Student No.:50
Time:Tue 10:00-11:30, 2017-3-7~2017-6-13
Instructor:Si Li, Zhengyu Zong  
Place:Conference room 3, Floor 2, Jin Chun Yuan West Building
Starting Date:2017-3-7
Ending Date:2017-6-13
Date: Tue 2017-4-25



Speaker: Jie Tu (CMS, Zhejiang University )



Time: 10:30-12:00



Place: Conference room 3, Floor 2, Jin Chun Yuan West Building




Title: The Deformation of Pairs (X,E) Lifting from Base Family




Abstract: In this talk, I will introduce my joint work with K.F. Liu on the analytic deformation theory of pairs (X,E), where X is a compact complex manifold and E is holomorphic vector bundle over X.



The splitting of holomorphic cotangent bundle via any integrable connection de- composes the Beltrami differential of pairs into the horizontal part and the vertical part. The horizontal part is the Beltrami differential of base family {Xt}. When the vertical part is vanishing under the decomposition by a Nakano semi-positive Chern connection ∇, i.e. {(Xt , Et )} is lifting from base family {Xt } via ∇, we get a infinitesimal extension of ∂ ̄-closed bundle valued (n, q)-form by the recursive method.




Date: Tue 2017-4-11


Speaker: Chunle Huang 黄春乐(Zhejiang University


Time: 10:30-12:00


Place: Conference room 3, Floor 2, Jin Chun Yuan West Building


Title: Logarithmic vanishing theorems on compact K\"{a}hler manifolds


Abstract: We will first establish an $L^2$-type Dolbeault isomorphism for logarithmic differential forms by H\"{o}rmander's $L^2$-estimates. By using this isomorphism and the construction of smooth Hermitian metrics, we obtain a number of new Akizuki-Kodaira-Nakano type vanishing theorems for sheaves of logarithmic differential forms on compact K\"ahler manifolds with simple normal crossing divisors, which generalize several classical vanishing theorems, including Norimatsu's vanishing theorem, Gibrau's vanishing theorem, Le Potier's vanishing theorem and a version of the Kawamata-Viehweg vanishing theorem.



Date: 2017-3-28


Speaker: Baosen Wu 吴宝森YMSC


Time: 10:30-12:00


PlaceConference room 3, Floor 2, Jin Chun Yuan West Building


Title: Construction of stable sheaves via Serre correspondence


Abstract: Serre correspondence is a classical tool to construct rank 2 vector bundles or coherent sheaves with prescribed Chern classes. However, testing the stability of such bundles is in general very difficult. We shall work on Calabi-Yau threefolds and use deformation to show the stability of such bundles or sheaves.



Date: 2017-3-14


Speaker: 曹亚龙


Time: 10:00-11:30


Place: Conference room3, Floor 2, Jin Chun Yuan West Building


Title: Gopakumar-Vafa type invariants for Calabi-Yau 4-folds




As an analogy of Gopakumar-Vafa conjecture for CY 3-folds, Klemm-Pandharipande proposed GV type invariants on CY 4-folds using GW theory and conjectured their integrality. In this talk, we propose a sheaf theoretical interpretation to these invariants using Donaldson-Thomas theory on CY 4-folds. This is a joint work with Davesh Maulik and Yukinobu Toda.



Date: 2017-3-7


Speaker: Sz-Sheng Wang 王赐圣(YMSC


Title: Towards decompositions of small transitions of Calabi-Yau threefolds


Abstract: Let \pi : \hat{X} \to X be a small projective resolution of a Calabi--Yau 3-fold X, which has terminal singularities. If X can be smoothed to a Calabi--Yau manifold \tilde{X}, then the process of going from \hat{X} to \tilde{X} is called a small transition.

In order to decompose small transitions, we introduce a subclass of small transitions which we call“primitive”small transitions and study such subclass. More precisely, we show that if the natural closed immersion of miniversal deformation spaces Def(\hat{X}) \hookrightarrow Def(X) is an isomorphism then X has only ordinary double points as singularities. A determinantal construction of conifold transition will also presented, if there is enough time.