中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
学术报告
多复变与复几何研讨班
SCV&CG Seminar
Speaker: 曹俊彦 教授 (Université Côte D'Azur, Laboratoire J.A. Dieudonné)
Language: Chinese
Title: Hodge Theory in Singular Settings and Some Applications（I）
Time & Venue: 2025年12月24日（星期三） 10:00 - 11:30 & 南楼N913
Abstract: Hodge theory plays an important role in complex geometry. In this lecture series, I will explain Hodge theory in certain singular and twisted settings, along with several applications. The lectures are based on some joint works with M. Păun and a recent joint work with Y. Deng, C. Hacon, and M. Păun.
In the first lecture, I will introduce Hodge theory in the conic setting. As an application, I will explain how to use it to prove a logarithmic version of the injectivity theorem.
In the second lecture, I will discuss additional applications, including the invariance of plurigenera and properties of the jumping loci for pluricanonical systems.
In the third lecture, I will present Hodge theory in the logarithmic setting with a rank-one local system. In particular, we establish a strong Hodge decomposition for a rank one local system with a mixed conic-Poincaré metric.
In the final lecture, I will discuss further applications.
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Title: Hodge Theory in Singular Settings and Some Applications（II）
Time & Venue: 2025年12月25日（星期四） 19:00 - 20:30 & 南楼N913
Abstract: Hodge theory plays an important role in complex geometry. In this lecture series, I will explain Hodge theory in certain singular and twisted settings, along with several applications. The lectures are based on some joint works with M. Păun and a recent joint work with Y. Deng, C. Hacon, and M. Păun.
In the first lecture, I will introduce Hodge theory in the conic setting. As an application, I will explain how to use it to prove a logarithmic version of the injectivity theorem.
In the second lecture, I will discuss additional applications, including the invariance of plurigenera and properties of the jumping loci for pluricanonical systems.
In the third lecture, I will present Hodge theory in the logarithmic setting with a rank-one local system. In particular, we establish a strong Hodge decomposition for a rank one local system with a mixed conic-Poincaré metric.
In the final lecture, I will discuss further applications.
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Title: Hodge Theory in Singular Settings and Some Applications（III）
Time & Venue: 2025年12月27日（星期六） 10:00 - 11:30 & 南楼N913
Abstract: Hodge theory plays an important role in complex geometry. In this lecture series, I will explain Hodge theory in certain singular and twisted settings, along with several applications. The lectures are based on some joint works with M. Păun and a recent joint work with Y. Deng, C. Hacon, and M. Păun.
In the first lecture, I will introduce Hodge theory in the conic setting. As an application, I will explain how to use it to prove a logarithmic version of the injectivity theorem.
In the second lecture, I will discuss additional applications, including the invariance of plurigenera and properties of the jumping loci for pluricanonical systems.
In the third lecture, I will present Hodge theory in the logarithmic setting with a rank-one local system. In particular, we establish a strong Hodge decomposition for a rank one local system with a mixed conic-Poincaré metric.
In the final lecture, I will discuss further applications.
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Title: Hodge Theory in Singular Settings and Some Applications（IV）
Time & Venue: 2025年12月28日（星期日） 19:00 - 20:30 & 南楼N913
Abstract: Hodge theory plays an important role in complex geometry. In this lecture series, I will explain Hodge theory in certain singular and twisted settings, along with several applications. The lectures are based on some joint works with M. Păun and a recent joint work with Y. Deng, C. Hacon, and M. Păun.
In the first lecture, I will introduce Hodge theory in the conic setting. As an application, I will explain how to use it to prove a logarithmic version of the injectivity theorem.
In the second lecture, I will discuss additional applications, including the invariance of plurigenera and properties of the jumping loci for pluricanonical systems.
In the third lecture, I will present Hodge theory in the logarithmic setting with a rank-one local system. In particular, we establish a strong Hodge decomposition for a rank one local system with a mixed conic-Poincaré metric.
In the final lecture, I will discuss further applications.
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