* 일시 : 2023년 7월 11일 (화), 17시-18시

* 장소 : 종합과학관 A동 317호

* 연사 : 김기현 박사 (IHES(프랑스 고등과학연구소))

* 강연 제목 : Rigidity of long-term dynamics for the self-dual Chern-Simons-Schrödinger equation within equivariance

* 초록 : We consider the long time dynamics for the self-dual Chern-Simons-Schrödinger equation (CSS) within equivariant symmetry. Being a gauged 2D cubic nonlinear Schrödinger equation (NLS), (CSS) is L2-critical and has pseudoconformal invariance and solitons. However, there are two distinguished features of (CSS), the self-duality and non-locality, which make the long time dynamics of (CSS) surprisingly rigid. For instance, (i) any finite energy spatially decaying solutions to (CSS) decompose into at most one (!) modulated soliton and a radiation. Moreover, (ii) in the high equivariance case (i.e., the equivariance index ≥ 1), any smooth finite-time blow-up solutions even have a universal blow-up speed, namely, the pseudoconformal one. We explore this rigid dynamics using modulation analysis, combined with the self-duality and non-locality of the problem.