报告题目：A new index theory for linear self-adjoint operator equations and its applications
报告摘要：Recently, with the idea of I.Ekeland and Dong, we develop an index theory for linear self-adjoint operator equation with the linear self-adjoint operator A has no compact resolvent. As applications, we consider the existence and multiplicity of periodic solutions of wave equations and beam equations.
报告题目：ADMM for Big Data Convex Optimization
报告摘要：Optimization problems in machine learning, compressed sensing, social network science, computational biology and other prominent application domains always contain millions or billions of variables. Classical optimization algorithms are not designed to scale to instances of this size; new approaches are highly urgent. This talk aims to analyze the structure of the convex optimization problems from its primal or dual formulation and review the latest symmetric Gauss-Seidel based ADMM in Big Data setting. The applications of ADMM in inverse covariance estimation, sparse MRI image reconstruction, transform invariant low-rank texture are also discussed.
报告题目：Bistability and multistability in election game dynamics models and HIV infection dynamics models
In this talk, we analyze a few opinion formation or election game dynamics models. Fora simple model with two subpopulations with opposing opinions A and B , if the fraction of committed believers of opinion A (“A zealots”) is less than a critical value, then the system has two bistable equilibrium points. When the fraction is equal to the critical value, the system undergoes a saddle-node bifurcation. When the fraction is larger than the critical value, a boundary equilibrium point is globally asymptotically stable, suggesting that the entire population reaches a consensus on A . We ?nd a similar bistability property in the model in which both opinions have their own zealots. We also extend the model to in clude multiple competitors and show the dynamical behavior of multistability. The more competitors subpopulation A has, the fewer zealots opinion A needs to obtain consensus. This work is joint with Jianhong Wu and Libin Rong.