Program
 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: 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

Abstract:

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.