Today is 17/03/2020.

Since I have gone too lazy these days without learning not as much mathematics each day, I decide to try to make one post per day (OPPD) (or may be per two days if busy) telling about what I learned. It won’t be like many mathematicians’blogs you find online but rather just like a normal blog/diary.

What do I currently want to learn?

Following the flow of mathematics community at my university, below are things I want to learn first:

  1. (Linear) algebraic groups / Lie algebras and representations. Right know, I think this is the most important thing I need to learn first (as you will see next items in the list all related to this). Here is what I plane to prioritise first:
    1. First, I want to learn classification of representations of semisimple Lie algebras.
    2. Next will be learn structure theory of reductive groups (?), but since this require some algebraic geometry, I may need to learn those first. This serves as the prereq for the 3rd item in this list.

  2. Symmetric functions and related areas. I am currently following Macdonald’s book and see how far I go first. I also need to write a report about this so this One post per day might be useful motivating me to write the report.

  3. Representation of (reductive?) p-adic groups Something along those lines. For now I am following Bushnell and Henniart Local Langlands for GL(2) with very slow reading speed. But I realized many other notes follow have some parts (say Parabolic induction, Jacquet functor) in generality for general reductive $p$-adic groups(?) instead of $GL_2(F)$ so I am hesitating what to choose to get the best out of it. That is the first item in this list is very important right now.

  4. Crystal bases. We have a reading course about this in our university. So there are two books: Hong and Kang, the other by Bump and Schilling. We follow Bump and Schilling in our reading course, focusing mostly on the combinatorics part of it. In this blog I will see how much I learn from these two books and post this here. I also need to present some material from one of these books.

  5. Cluster algebras. See Gregg Musiker’s website for a lot of references. Right now I plan to follow Sergey Fomin, Laurent Williams, and Andrei Zelevinsky, Introduction to Cluster Algebras.

UPDATE 20/03/2020: OK it seems that due to COVID-19, two reading courses on Crystal bases and Cluster algebras are cancelled this semester. As a result, I will prioritise learning the first four items, leaving out cluster algebra if I have free time to do.

Why posting in blogs will help learning these?

I need some audiences (imaginary audiences also fine) to listen to me talking about this.