报告题目：Bounded Morse Index Solutions to Allen-Cahn Equation on Riemann Surfaces

报告时间：2023-05-19 16:00-17:00

报告人：魏军城 加拿大皇家科学院院士  加拿大英属哥伦比亚大学

报告地点：理学院东北楼四楼报告厅

Abstract：A recent result of Chodosh-Mantoulidis (Pub.IHES 2023) proved that the nodal sets of bounded Morse index solutions of Allen-Cahn equation on Riemann surfaces must be geodesic nets (with possibility of higher multiplicities). In this talk I will first discuss the construction of solutions on geodesic nets and the computations of the Morse index. Next we consider multiplicity two interfaces. We prove that necessary and (almost) sufficient condition for multiplicity two geodesic is the existence of bouncing Jacobi fields. Using variational methods we prove the existence of bouncing Jacobi fields and then compute the Morse index solutions with the index of bouncing Jacobi fields. (Joint work with Yong Liu and Frank Pacard.)