报告题目：Compatibility condition of PDE systems describing affinly homogeneous surfaces in \mathbb{C}^3 

报告人：陈张弛 ，中科院数学所

时间：2022年12月30日（星期五）下午14:30-16:00

腾讯会议：572-283-2445    会议密码：123456

摘要：Consider a smooth graphed holomorphic surface \{u=F(x,y)\} in \mathbb{C}^3_{x,y,u} under the action of the affine transformation group A_3(\mathbb{C}). A smooth surface in \mathbb{C}^3 is affinely homogeneous if there is a subgroup of A_3(\mathbb{C}) acting transversely on it. 

   In 1999, Eastwood and Ezhov classified all affinely homogeneous surfaces into a list by determining possible tangential vector fields. In 2020, with Merker J., we organise all homogeneous models in inequivalent branches. And we express the moduli of each branch as an algebraic variety.

   The main technique is to write down a complete system of differential invariants. A surface is homogenous only if its invariants are constant, which gives infinitely many PDEs. Using Fels-Olver's recurrence formula, all invariants can be generated by finitely many fundamental invariants of low orders. However, in some situation, all fundamental invariants being constant is not enough to determine homogeneity. Compatibility conditions, also known as Frobenius integrability conditions, shall also be included.