In this talk, I will give a brief introduction to the Cheeger-Colding theory. Firstly I review the definition of Gromov-Hausdorff distance and Gromov's precompactness theorem. Secondly I will focus on the three fundamental theorem in this field, i.e. Almost splittng theorem, Almost volume cone implying almost metric cone and volume continuity. I will explain the ideas to prove them. Finally I will mention some important applictions made by experts in this field and some open problems.

We study singular closed convex hypersurfaces with constant Weingarten curvature. The main result is two-folded: if the hypersurface with pointed singularities having $H_k=const$ for $1/leq k/leq n-1$ , then singularities are removable; while for k=n, there do exist singular convex hypersurfaces with constant Gaussian curvature, but if there are only two singular points, then the hypersurface must be a rotational symmetric football. This is a joint work with H. Fang and W. Wo

题目：我的数学历程报告人：石钟慈 院士 （中国科学院 数学与系统科学院）地点：致远楼107室时间：2017年6月2日 16：00-17：00欢迎各位参

题目：非紧Kahler流形的典则度量报告人：傅吉祥 教授 （复旦大学 必赢国际bwin登录）时间：2017年6月2日（周五）下午15：30-16:30地点：致远楼105室欢迎广大师生参加

We study optimal bandwidth selection in nonparametric cointegrating regression where the regressor is a stochastic trend process driven by short or long memory innovations. Unlike stationary regression, the optimal bandwidth is found to be a random sequence which depends on the sojourn time of the process. All random sequences that lie within a wide band of rates as the sample size goes to infinite have the property that local level and local linear kernel estimates are asymptotically normal

We consider a priori estimates of the Weyl's embedding problem of $(/mathbb{S}^2, g)$ in general $3$-dimensional Riemannian manifold $(N^3, /bar g)$. We establish mean curvature estimate under natural geometric assumption. Together with a recent work by Li-Wang, we obtain an isometric embedding of $(/mathbb{S}^2,g)$ in Riemannian manifold. In addition, we reprove Weyl's isometric embedding theorem in space form under the condition that $g/in C^2$ with $D^2g$ Dini continuous.

In this talk, we study a reaction-diffusion population model with time delay. We establish a comparison principle for coupled upper/lower solutions and prove the existence/uniqueness result for the model. We then show the global asymptotic behavior of the model.

In this talk, I will present some results on chemostat models. In particular, I will report some progress on competitive exclusion principle. In addition, I will also present some results on factors leading to transient oscillations in chemostat.