中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
Speaker: 金希深 讲师（中国人民大学）
Title: Chern number inequalities related to dHYM metrics
Time&Venue: 2024年12月6日（星期五） 9:00-10:00 & S315
Abstract:In this talk, I will talk about relations between the deformed Hermitian-Yang-Mills metrics and Chern number inequalities on 4-dimensional Kaehler manifolds. This is a joint work with Han and comfirms a conjecture of Collins-Yau.
Speaker: 李畅 副教授（中国人民大学）
Title: Rigidity of eigenvalues of shrinking Ricci solitons
Time&Venue: 2024年12月6日（星期五） 10:00-11:00 & S315
Abstract: We study the rigidity of eigenvalues of shring Ricci solitons. It is known that the drifted Laplacian on shrinking Ricci solitons has discrete spectrum, its eigenvalues have a lower bound and a rigidity result holds. We prove that if there exists some eigenvalues close to this lower bound, then the soliton almost splits as a product of some metric space with the Euclidean space. This is based on a joint work with Huaiyu Zhang and Xi Zhang.