AbstractNesterov's accelerated gradient descent (NAG) is one of the milestones in the history of first-order algorithms. Until recently, it was not successfully uncovered by the high-resolution differential equation framework in [Shi et al., 2021] that the mechanism behind the acceleration phenomenon is due to the gradient correction term. Along this way, I present some recent advances about th...
AbstractKey spaces in Toric Topology refer to a family of spaces that carry torus actions. They include moment-angle complexes, toric manifolds and orbifolds, partial quotients, and their real analogs. The study of toric spaces also stimulates the development of polyhedral products. In three talks, we aim to cover the following topics: 1) the fundamental properties of these key spaces, 2) tools...