We first recall some techniques of scalar curvature flow on Sn developed in my previous paper joint with Professor Xingwang Xu (Invent. Math. 2012). Next, we extend such a flow approach to prove a perturbation result of the fractional Nirenberg problem, i.e.

Deep learning has aroused extensive attention due to its great empirical success. The efficiency of the block coordinate descent (BCD) methods has been recently demonstrated in deep neural network (DNN) training.

Non-convex optimization is widely involved in many machine learning problems, and it usually implicates a two-stage algorithm: a refined initialization followed by a local gradient search.

I will first talk about the background and some well-known results of the beta ensemble. Then I will introduce the rigidity of eigenvalues for beta ensemble in multi-cut regime, i.e., the fact that each eigenvalue in the bulk is very close to its "classical location".