# 12-30【陈张弛】腾讯会议 可积系统与几何清华-科大联合学术报告

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.