Darboux theorem, symplectic factorization and ellipticity
数学专题报告
报告题目(Title)：Darboux theorem, symplectic factorization and ellipticity
报告人(Speaker)：Professor Bernard DACOROGNA (Federal Institute of Technology in Lausanne (EPFL), Switzerland)
地点(Place)：后主楼1124室
时间(Time)：2024年4月1日 下午16:00至17:00
邀请人(Inviter)：卢广存
报告摘要
(joint work with Wifrid GANGBO and Olivier KNEUSS):
(I) Our first result concerns Darboux theorem (1882) the starting point in symplectic geometry. We discuss the existence, regularity and uniqueness of solutions, emphasizing the role of ellipticity.
(II) We then apply the above result to the so-called symplectic factorization. We show that any map φ, satisfying appropriate assumptions, can be written as φ= ψχ where ψ preserves the standard symplectic form ωm and ▽χ is orthogonal to ωm.
(III) The analogy with mass transportation and the Monge-Ampère equation, as well as with the polar factorization, will be emphasized.
