Algebraic and geometric methods for algebraic differential equations
Speaker: Võ Ngọc Thiệu (Trường Đại học Tôn Đức Thắng)
Time: 9:30 - 11:30, May 12, 2021
Venue: Room 301, A5, Institute of Mathematics, VAST
Abstract: In this talk, we discuss three different approaches to attack the problem of determining symbolic solutions of an algebraic ordinary differential equation (AODE). The first approach is based on Newton polygon which is a tool for understanding the behaviour of the AODE over local fields. The second approach is based on an algebraic consideration of the AODE and tools from algebraic function field theory. The third approach relies on the consideration of the AODE as an algebraic variety over rational function field and parametrization theory of rational curves/surfaces. The strengths and weaknesses of each approach as well as related open problems will be discussed.