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Three Stories on the Modeling of Collective Dynamics

Speaker

Seung Yeal Ha, Department of Mathematical Sciences, Seoul National University

Time

2019.09.24 14:00-15:00

Venue

Room 306, No.5 Science Building

Abstract

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.