学术报告（李洪全 2026.1.13）

摘要：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}^kY_j^2, asexplicitly 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.