“代数与数论”暑期学校报告
报告人：恽之玮 (MIT)
题 目：从幂零矩阵谈起
时 间：2019.08.21（星期三）, 14:00-15:00
地 点：国科大中关村校区S106室
摘 要：幂零矩阵的相似类是一般线性群的幂零轨道,它可由整数拆分来分类。在李群理论和表示论中,幂零轨道扮演着至关重要的角色,对此我们将通过一些例子来阐述。最后我们试图回答以下问题:什么是幂零轨道在环群(loop group)中的对应物?
报告人：刘文飞（厦门大学）
题 目：On the canonical volumes of projective varieties
时 间：2019.08.21（星期三）, 15:15-16:15
地 点：国科大中关村校区S106室
摘 要：Canonical divisors are intrinsically defined on each normal variety. When the varieties are projective, the volumes of canonical divisors, called canonical volumes are used in the classification theory of projective varieties.In this talk, I will first explain the notion of canonical volumes and the basic ideas of how to compute them. Then I will address several geography problems concerning canonical volumes of various classes of projective varieties. Basically, these problems ask which numbers can be realized as the canonical volumes of projective varieties with certain prescribed constraints. Apart from the well-known results about smooth curves and surfaces, I will also touch upon singular surfaces and higher dimensional varieties, whose canonical volumes are only fractional numbers.
