First, we presents a basic decomposition method for a broad class of multi-block nonsmooth optimization problems subject to coupled linear constraints on the variables, which motivated by block partitioned problems arising from group sparsity representation and generalized non-cooperative potential

I will first review some universality results for Wigner matrices and sparse random graphs, and then talk about some recent development on the fluctuation of individial eigenvalues of these models.

It is well known that smooth solutions to the 2d Euler equation remain smooth and are globally defined. However the long time behavior of solutions is not well understood.

We demonstrate that for systems experiencing spontaneous (internal) symmetry breaking, the Quantum Yang Baxter Equations (QYBE) can be interpreted as the superposition of all the possible vacuum expectation values of the order parameter.