In this talk I will give a short survey on some interesting geometric integral formulas and inequalities, such as Minkowski integral formula, Heintze-Karcher inequality and isoperimetric inequalities etc. We will go over the idea of proofs and then propose some questions.

In this talk, we will show that some results on vector valuation. All SL(n) covariant vector valuations on convex polytopes in Rn are completely classified without any continuity assumptions. The moment vector turns out to be the only such valuation if n ≥ 3, while two new functionals show up in dimension two.

Flow method is an effective tool to study variational problems. In this seminar, we discuss Minkowski type problems and their related flow arguments.

We will talk about the Li-Tam theory by Peter Li and Luen-Fai Tam (J. Differential Geometry Vol 35(1992), 359-383 ), which relates the infinity geometric structure of complete manifolds to the theory of harmonic functions.

针对长时间（15年）运行卫星智能配电元器件，研究自适应预测关键指标的优化采样贝叶斯方法和似然方法，给出获取优化稳健预测关键指标的有效数据集的方法，以及预测关键指标的方法。通过示例展示了应用所给方法获得的采样数据和有效数据集的特性。进一步证明了非独立数据下关键指标预测的概率收敛性。将所得方法应用与天宫系列卫星智能配电元器件的指标预测。

In this lecture, we will introduce the basic definitions and summarize some main results on the value distribution theory of algebroid functions. The results focus on the singular directions, filling discs, uniqueness theorems. These results are compared with the case of meromorphic functions. Some open problems are also proposed.

Random genetic drift occurs at a single unlinked locus with two or more alleles. The probability density of alleles is governed by a degenerated Fokker-Planck equation. Due to the degeneration and convection, Dirac singularities will always be developed at boundary as time evolves, which is just the so-called fixation phenomenon. In order to find a complete solution which should keep the conservation of positivity, total probability and expectation, different schemes of FDM, FVM and FEM are tested to solve the equation numerically. We observed that the methods have totally different long-time behaviors. Some of them are stable and keep the conservation of positivity and probability, but fail to keep the expectation. Some of them fails to keep the positivity.

In this talk, we will revisit the Heterogeneous Multiscale Methods(HMM) for homogenization of elliptic problems. Firstly we talk about the relationship between HMM and other multiscale methods such as Variational Multiscale Methods, Multiscale Finite Element Methods and Free Bubble Methods. Then we discuss the error analysis for problems without scale separation.