Cousin problems for overdetermined systems of partial differential equations.

讲座时间 Datetime: 2022年9月6日，星期二，14:30-15:30

地点 Venue: 腾讯线上会议：504-422-717

主持人 Host：邵国宽

报告人 Speaker: 嵇庆春 

单位 Affiliation: 复旦大学

报告摘要 Abstract:

 The talk is based on joint work with J.Yao and G.S.Yu. We construct a resolution of the sheaf of germs of solutionsof a overdetermined system of PDEs. A sufficient condition for global exactness is obtained in terms of semi-positivity and a lower bound of the rank of a quadratic form which was originally introduced by L.Hörmander. As applications of global exactness, we investigate the original overdetermined system by formulating Cousin type problems which provide approaches to gluing local solutions of overdetermined systems of PDEs.