应理学院数学系邀请，黑龙江省数学会理事长薛小平教授，将于5月19日至5月21日访问我校数学系，期间将作一场学术报告，欢迎感兴趣的学生和老师参加。

报告时间：2017年5月19日（周五）上午9:00-10:00

报告地点：主楼东配楼203室（数学系报告厅）

报告题目：Gradient Systems and its Applications

报告摘要：The Lojasiewicz inequality and Lojasiewicz exponent reveal a fundamental relation between a potential function and its gradient system. In this talk, I explore the Lojasiewicz exponent of Kuramoto model and prove that the exponent is exactly 1/2 for equilibria located inside a quarter of circle. This implies that the convergence towards such a phase-locked state must be exponentially fast. In contrast, we give an example to see the exponent can be less than 1/2 for other equilibriums. More precisely, we prove that the exponent for the bi-cluster equilibrium, which is located on the boundary of a quarter of circle, is 1/3. This gives an insight for the occurrence of exponential and algebraic convergence of Kuramoto model. I also present a general theorem for exponential convergence of second-order gradient-like system, by which a criterion for the Kuramoto model with inertia is established.