中科院数学与系统科学研究院

数学研究所

学术报告

数论研讨班

报告人:孙玉奇（内蒙古大学）

题  目：On coarse isometries and linear isometries of Banach spaces

时  间：2024.07.18（星期四）15：00-16：00

地  点：N820

报告人:Fangchi Yan（Department of Mathematics, Virginia Tec）

题  目：Well- posedness of initial-boundary value problems for the Korteweg- de Vries equation

时  间：2024.07.19（星期五）10：00-11：00

地  点：N820

摘 要：Nonlinear dispersive equations, such as the Korteweg- de Vries (KdV) equation, play a crucial role in describing wave phenomena in nature, such as shallow water waves. However, solving the initial-boundary value problems of these equations, particularly ensuring the existence, uniqueness, and stability of solutions, is a highly challenging mathematical problem. This talk will introduce our recent progress in studying the well- posedness of initial-boundary value problems for the KdV equation and its generalizations.

报告人:David R. Larson（Department of Mathematics, Texas A&M University）

题  目：Frames generated by representations of semigroups

时  间：2024.07.22（星期一）9：30-10：30

地  点：N820

摘 要：We first discuss an early result of the speaker and D.Han that completely characterizes the similarity classes of frames generated by the action of a group of operators on a Hilbert space in terms of the unitary group of a von Neumann algebra. Then we obtain a canonical form for frames generated by a semigroup action. This is related to recent work of Aldroubi, Christensen, et.al., on dynamical sampling frames.