Sharp Heat Kernel bounds on M´etivier Groups: the influence of non-trivial abnormal geodesics

讲座题目：Sharp Heat Kernel bounds on M´etivier Groups: the influence of non-trivial abnormal geodesics
讲座时间 Datetime: 2026年1月22日，周四，14：00 - 15：00
地点 Venue: 海琴二号A457 
主持人 Host：黄山林 副教授
报告人 Speaker: 李洪全 教授

单位 Affiliation: 复旦大学
报告摘要 Abstract:  Let H(2n, m) denote the Heisenberg-type group whose center has dimension m ≥ 2, and ∆_csl its canonical (homogeneous) sub-Laplacian. Let Y_1, . . . , Y_k (1 ≤ k ≤ m − 1) are linearly independent in the center of the left-invariant Lie algebra. We establish precise estimates for the heat kernel associated with the operator ∆_csl + \sum_{j = 1}^k Y_j^2, as explicitly as we can hope for. Compared with the well-studied cases where k = 0 (i.e. the canonical sub-Riemannian heat kernel) and k = m (i.e. the generalized Riemannian
heat kernel w.r.t. ∆_csl), our intermediate cases become drastically difficult due to the
existence of non-trivial abnormal geodesics (albeit not strictly abnormal ones). The work is in collaboration with Yimeng Chen.

报告人简介：
李洪全，复旦大学数学科学学院教授、博士生导师，国家杰出青年科学基金获得者，上海市“东方学者”特聘教授。其主要研究方向为流形上的调和分析，在Riesz变换、极大函数、热核与热半群梯度估计等方面取得了系列具有重要意义的研究成果。相关成果发表在《Journal für die reine und angewandte Mathematik》《Journal de Mathématiques Pures et Appliquées》《Mathematische Annalen》《Transactions of the American Mathematical Society》《Mathematische Zeitschrift》《Journal of Functional Analysis》《Communications in Partial Differential Equations》等国际权威学术期刊上。