We have the following seminar via google meet.
Title: Uniform-in-time continuum limit of the lattice Winfree model and emergent dynamics
Time: January 13th (Wednesday) 10:00 – 10:40
Speaker: Myeongju Kang (Seoul National University)
Abstract: We study a uniform-in-time continuum limit of the lattice Winfree model(LWM) and its asymptotic dynamics which depends on system functions such as natural frequency function and coupling strength function. The continuum Winfree model(CWM) is an integro-differential equation for the temporal evolution of Winfree phase field. The LWM describes synchronous behavior of weakly coupled Winfree oscillators on a lattice lying in a compact region. For bounded measurable initial phase field, we establish a global well-posedness of classical solutions to the CWM under suitable assumptions on coupling function, and we also show that a classical solution to the CWM can be obtained as a $L^1$-limit of a sequence of lattice solutions.
Title: Emergence of consensus on the Stiefel manifold
Time: January 13th (Wednesday) 10:45 – 11:25
Speaker: Dr. Dohyun Kim (Seoul National University)
Abstract: In this talk, we introduce first-order and second-order high-dimensional Kuramoto models on the Stiefel manifold which extend the previous consensus models on Riemannian manifolds including several matrix Lie groups. For the proposed models, sufficient frameworks leading to complete and practical consensus are provided in terms of the initial data and system parameters. On the other hand, we propose a consensus-based algorithm for nonconvex optimization on the Stiefel manifold. For a given objective (or target) function on the Stiefel manifold, we construct a stochastic interacting particle system for sample points which are expected to converge to a single point, which is close enough to a global minimizer.