中科院数学与系统科学研究院
数学研究所
代数几何研讨班
报告人：江辰 青年研究员（复旦大学）
题 目：Explicit boundedness of canonical Fano 3-folds: known results and open problems
时 间：2021.6.22（星期二），9:00-10:00
地 点：思源楼 817
摘 要：Motivated by the classification of canonical Fano 3-folds, we are interested in various boundedness results of canonical Fano 3-folds. I will summarize the known results and open problems in this area.
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报告人：方江学 副教授（首都师范大学）
题 目：Composition series for GKZ-systems.
时 间：2021.6.23（星期三），13:30-14:30
地 点：思源楼 817
摘 要：The hypergeometric functions were introduced by Euler as a power series in one variable. Gauss studied hypergeometric functions as solutions of the hypergeometric differential equationon the complex plane. Riemann give a complete description of the monodromy group for Gauss hypergeometric function. The monodromy group of a linear differential equation in the complex plane characterizes the behavior of the analytic continuation of its solutions. After them, people had introduced many generalizations of Gauss hypergeometric functions by increasing the number of parameters or the number of variables or both. In 1980s, Gelfand, Kapranov and Zelevinsky generalized the hypergeometric function in a unified way. They associated to any matrix A with integer entries a system of partial differential equations whose solutions are hypergeometric functions, which are now called the GKZ-systems or A-hypergeometric D-modules. In this talk, I will review some basic results of the Gauss hypergeometric functions and the GKZ-systems. Especially, I will construct a filtration on the GKZ-system with semisimple subquotients.
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