Seung Yeal Ha, Department of Mathematical Sciences, Seoul National University
Room 306, No.5 Science Building
In this talk, we briefly discuss three topics such as the universality of the collective dynamics, second-order Cucker-Smale flocking on Riemannian manifolds and a generalized aggregation model for the ensemble of rank-m tensors with the same size. In our first story, we discuss universal triality relation between bacteria aggregation, Cucker-Smale flocking and Kuramoto synchronization. These three seemingly different phenomena can be integrated into a common nonlinear consesnsus framework. In our second story, we present a second-order Cucker-Smale modeling on Riemannian manifolds such as the unit circle, the unit sphere in R^2 and Poincare upper half plane model for hyperbolic geometry. Finally, in our third story, we introduce a new unified model for the ensemble of aggregation of tensors with the same rank and size. Our new model includes previous well-known mathematical models such as the Kuramoto model, the Lohe type models as special cases.