Perspectives in Algebraic and Complex Geometry
January 19-21, 2018, Xiamen University

This workshop aims to bring together experts to survey and to communicate on new perspectives in algebraic and complex geometry. It is sponsored by School of Mathematical Sciences at Xiamen University and the Recruitment Program for Young Professionals. Anyone is welcome. If you would like to request funding, please email either of two organizers listed in below.

Organizers:

Wenfei LIU (刘文飞) Email:wliu@xmu.edu.cn;     Bo YANG (杨波) Email:boyang@xmu.edu.cn.

Invited Speakers:

  • Meng CHEN (陈猛) (Fudan University)

  • Zhi JIANG (江智) (Fudan University)

  • Dali SHEN (沈大立) (IMPA)

  • Xiaotao SUN (孙笑涛) (Tianjin University)

  • Tong ZHANG (张通) (East China Normal University)

    Schedule


    All lectures will be in 海韵实验楼105。 地点:曾厝垵西路1号厦门大学海韵园

    Jan 19th Jan 20th Jan 21st
    9:15-9:30 Opening Remark None None
    9:30-10:30 Meng CHEN Xiaotao SUN Meng CHEN
    10:30-10:45 Group Photo/Break Break Break
    10:45-11:45 Xiaotao SUN Meng CHEN Xiaotao SUN
    Lunch Lunch Lunch
    14:30-15:30 Zhi JIANG Dali SHEN Free afternoon
    15:30-15:45 Break Break
    15:45-16:45 Dali SHEN Tong ZHANG
    16:45-17:00 Break Break
    17:00-18:00 Tong ZHANG Zhi JIANG
    Dinner


    Abstracts

  • Meng CHEN

    Title: The explicit aspect of pluricanonical maps of projective varieties.

    In this series of lectures, we explain some methods and ideas in obtaining explicit birationality of pluricanonical maps of projective varieties with canonical singularities. Lecture 1 devotes to introducing the motivation and main results. In Lecture 2, we explain the generalized Koll\'ar's method on studying pluricanonical systems of projective varieties of general type. Lecture 3 is set for explaining the anti-canonical geometry of Q-Fano 3-folds.

  • Zhi JIANG

    Title: Decomposition formula in generic vanishing theory and its geometric applications.

    Abstract: I will describe a decomposition formula in generic vanishing theory due to Chen and myself, Pareschi-Popa-Schnell and explain in various context that how to apply this formula to deal with concrete geometric problems.

  • Dali SHEN

    Title: Geometry of ball quotients.

    Abstract: A quotient space of the complex hyperbolic space by a discrete subgroup of its automorphism group with finite covolume is usually called a ball quotient. In the first talk, I will give a gentle introduction to the geometry happened on ball quotients, such as their construction problem, compactifications, modular interpretations, as well as a little bit from differential geometric point of view. In the second talk, I will explain a joint work, with G. Heckman and E. Looijenga, on the theory of geometric structures on (toric) arrangement complements, which provides a more general viewpoint for the construction of ball quotients comparing to the classical hypergeometric system method.

  • Xiaotao SUN

    Title: Frobenius map and moduli spaces of parabolic sheaves.

    Abstract: For a variety over a field of characteristic p>0, it is an important question if it is globally F-regular. A globally F-regular variety has good singularities and has very nice vanishing theorems of cohomology. The theory also apply to varieties defined over a field of characteristic zero. A variety over a field of characteristic zero is called of globally F-regular type if its modulo p-reduction are globally F-regular for almost p. In this series of talks, I will review the theory of Frobenius splitting varieties and its generalization, globally F-regular varieties. Then I will prove that moduli spaces of parabolic bundles and generalized parabolic sheaves with fixed determinant over a curve are of globally F-regular type. Some open questions will be discussed.

  • Tong ZHANG

    Title: Geography of irregular varieties of general type.

    Abstract: In the two lectures, I will start from a brief survey of the geography of complex (irregular) surfaces of general type. Via a different method, it can be proved that some results over complex numbers hold also in positive characteristics. Then I will introduce the higher dimensional Severi inequality for varieties of maximal Albanese dimension and discuss the proof which relies on the aforementioned new method. Finally, I will talk about some new results beyond the Severi inequality.

    Invited Participants

  • Jinxing CAI (蔡金星) (Peking University)

  • Jingshan CHEN (陈敬珊) (Peking University)

  • Meng CHEN (陈猛) (Fudan University)

  • Yifan CHEN (陈伊凡) (Beihang University)

  • Yifei CHEN (陈亦飞) (AMSS)

  • Rong DU (杜荣)(East China Normal University)

  • Xinyi Fang (方馨怡)(East China Normal University)

  • Yun GAO (高云) (Shanghai Jiaotong University)

  • Cheng GONG (龚成) (Soochow University)

  • Yi GU (顾怡) (Soochow University)

  • Jie Hong (洪杰) (East China Normal University)

  • Xiaowen HU (胡晓文) (Sun Yat-sen University)

  • Zhi JIANG (江智) (Fudan University)

  • Sichen LI (李思辰) (East China Normal University)

  • Xiaohu LI (李小虎) (East China Normal University)

  • Zhan LI (李展) (Peking University)

  • Dun LIANG (梁钝) (Sun Yat-sen University)

  • Songbo LING (凌松波) (Peking University)

  • Jun LU (陆俊)(East China Normal University)

  • Dali SHEN (沈大立) (IMPA)

  • Jie SUN (孙洁) (Jianghan University)

  • Xiaotao SUN (孙笑涛) (Tianjin University)

  • Yongtao Wang (王永韬) (East China Normal University)

  • Xiaoxing WU (吴小行) (East China Normal University)

  • Jinsong XU (许劲松) (Xi'an Jiaotong Liverpool University)

  • Jinxing XU (许金兴) (University of Science and Technology of China)

  • Xun YU (余讯) (Tianjin University)

  • Yao YUAN (袁瑶) (Tsinghua University)

  • Lei ZHANG (张磊) (Shaanxi Normal University)

  • Tong ZHANG (张通) (East China Normal University)

  • Yi ZHANG (张毅) (Fudan University)

  • Hang ZHAO (赵航) (Peking University)

  • Ran ZHAO (赵然) (East China Normal University)

  • Huaiqing ZUO (左怀青) (Tsinghua University)


    Last modified: 12/22/2017.