## Bài đăng

### Seminar Cartan (phần 2) - Đại số phân bậc vi phân

Trong phần này, mình (em) sẽ trình bày lại những chi tiết trong bài nói của Cartan, DGA-algebres et DGA-modules. Giả sử $\Lambda$ là một vành giao hoán có đơn vị.Khái niệm đại số phân bậcĐịnh nghĩa. Một $\Lambda$-đại số phân bậc là một $\Lambda$-đại số và các module con $A_k (k \geq 0)$ sao cho $1 \in A_0$. Mỗi phần tử $x$ trong $A_k$ được gọi là thuần nhất bậc $k$, ta kí hiệu $\left |x \right| = k$ và chỉ dùng kí hiệu này khi ám chỉ phần tử thuần nhất.

### Workshop 'The Mordell-Weil theorem' and something I have learnt

I write this post to summarize something I was particularly interested in during the Mordell-Weil theorem workshopin Tuan Chau, Quang Ninh held by the Institute of Mathematics two days ago. The workshop provides the most fundamental concepts of arithmetic of ellitpic curves over number fields and ends up with the proof of the famous Mordell-Weil theorem asserting that the group of rational points on an elliptic curves over number field is finitely generated. The so-called method Galois-descent was presented which allows us compute the Mordell-Weil group in certain 'good' cases. All follows Silverman's text on elliptic curves.
There are totally 10 talks, starting with my talk about algebraic varieties, actually, recently I am quite swamped in other researches on complex geometry so I just chose the most intelligible one, that you could say my talk is superfluous. After my talk, there are two talks are about basic properties of curves such as Riemann-Roch, isogenies, ...Some …

### Computational examples with Chern characteristic classes

This blog post is where I shall list my favourite examples about the applications of characteristic class, particularly about Euler class and Chern classes. Rather than stressing theoretical aspects, I would like to provide practical examples based on my own experience, most of them could be found in standard textbook or math-stackexchange but I do not really remember the source, just type everything. I would also update the post whenever I see a new useful exampleSo I may assume you guys are familiar with the definitions of either Euler or Chern classes. Usually, there are two kinds of definitions. The first one is from differential geometry point of view, via Chern-Simon theory and the other one is given by Grothendieck, more ad hoc, of course, which presents a list of axioms. It is encouraged everyone should know both approachs. The second seems to be easier at first but gradually become quite difficult for newbie to figure and does any concrete example. Characteristic classes, ver…