ECUST Algebraic Geometry and Complex Geometry Seminar
Organizer: Sichen Li (ECUST)
The purpose of this seminar is to introduce recent results on algebraic geometry and complex geometry since 2023 Fall.
If you are interested in giving a talk on your results, please contact the organizer(sichenli@ecust.edu.cn).
2023 Fall
Time: 2023,Oct. 27 (FRI), 15:30-16:30 (Beijing)
Location: D302,Fengxian Campus
Speaker: Min-Jie Luo (Donghua University)
Title: Fractional Calculus: From Classical Theory to Forefront
Abstract: In this talk, we first give a brief review of the early development of the Fractional Calculus. Then, based on the well-known results of Saigo and Kiryakova, we show the core idea of the Generalized Fractional Calculus and illustrate how it has evolved over the last few decades to become an important part of the modern theory of Fractional Calculus. We also report our latest work on a certain class of fractional integral operators whose kernels involve a very special class of generalized hypergeometric functions. Finally, we point out some problems for further research.
Time: 2023, Oct. 20 (FRI), 16：00-17：00 (Beijing)
Location: Room 505, Building No. 8, Xuhui Compus
Speaker: Xin Lu (East China Normal University)
Title: Strict Arakelov inequalities for a semi-stable fibration
Abstract: The classical Arakelov inequality is key to the Shafarevich conjecture. It gives an upper bound for the degree of the Hodge bundle of a semi-stable fibration of curves in terms of the base curve and the discriminant. Later on, such type inequalities are extended to higher dimension and to Higgs bundles. In this talk, I will talk about the development of these Arakelov inequalities and the strictness in certain cases. It is based on joint works with Ke Chen, Sheng-Li Tan, Jin-Bang Yang, and Kang Zuo.
Time: 2023, Oct. 20 (FRI), 14：45-15：45 (Beijing)
Location: Room 505, Building No. 8, Xuhui Compus
Speaker: Chen Jiang (Fudan University)
Title: Geography of varieties of general type
Abstract: We study birational invariants in order to study birational classifications of varieties. Geography is the study of relations among different invariants. We will focus on two fundamental invariants: canonical volume and geometric genus. For surfaces there are classical results such as Miyaoka-Yau inequality and Noether inequality. I will discuss higher dimensional analogue of them, and introduce our recent work on the optimal Noehter inequality for 3-folds joint with Jungkai Chen and Meng Chen.
Time: 2023,Oct.20 (FRI), 13：30-14：30 (Beijing)
Location: Room 505, Building No. 8, Xuhui Compus
Speaker: Zhengyu Hu (Chongqing University of Technology)
Title: 代数簇的极小模型纲领及其推广
Abstract:极小模型纲领是三维及更高维的代数簇分类理论中的核心理论之一。在报告中我将简介其主要发展，并介绍它在2016年后的推广，尤其是广义极小模型理论这项来自Zariski分解与纤维丛的技术推广。我还将介绍我们近期的一些更广泛的推广及其与模空间的联系。部分工作是与C.Birkar的合作进展。