勷勤数学•专家报告

题      目：Random tensors and general dispersive equations

报  告  人： 梁锐 博士  (邀请人：李颖花)

                                     University of Massachusetts Amherst

时      间： 1月15日  10：00-11:00

地     点：数科院东楼401

报告人简介:

        梁锐博士毕业于英国伯明翰大学，现为美国马萨诸塞大学阿默斯特分校数学与统计系访问助理教授。其研究方向为非线性偏微分方程与调和分析。研究工作结合偏微分方程、调和分析与概率方法，探讨方程解的适定性问题，包括解的存在性、唯一性与稳定性。同时关注不变测度与 Gibbs 测度的构造及其动力学性质，以及不同背景下的 Strichartz 估计。近来，研究兴趣拓展至构造性量子场论相关方向。研究成果发表在 SIAM Journal on Mathematical Analysis 和 Communications in Mathematical Physics 上。

摘      要：

        In this talk, we consider the Schrödinger equation with a cubic nonlinearity on the circle, with initial data distributed according to the Gibbs measure. We discuss the challenges and strategies involved in establishing the Poincaré recurrence property with respect to the Gibbs measure in the full dispersive range. Using the theory of the random averaging operator developed by Deng–Nahmod–Yue (2019), this work addresses an open question posed by Sun–Tzvetkov (2021). We also explain why the Gibbs dynamics in the full dispersive range is sharp in a certain sense. Finally, we show how the theory of random tensors can be used to extend this result to general dispersive equations in multi-dimensional settings.

          欢迎老师、同学们参加、交流！