SIMO Retiree Blog

(Jit here). Today I want to explain how to prove Skolem-Mahler-Lech using the p-adic numbers, and explain some sort of generalization in the area of algebraic/arithmetic dynamics, known as the Dynamical Mordell-Lang conjecture, which is still an open problem.

(Dylan here.) 0. Introduction This post will be a bit adventurous, but hopefully the risk will pay off. As I am excited to jump into the main content, my introduction/message will be brief: I wish to convince you that everything can be put into words and pictures, even fuzzy intuition. I will attempt to do so by rambling abstractly about ideas that I believe I have understood to some extent, and I think are beautiful.

(David here!) I was reading up about chip-firing recently ( this article is great), and I realized that the main theorem used the trick of looking at the configuration space, which is really interesting but rarely used. As a quick recap: the setting of chip-firing places a number of chips on the vertices of a graph, and if a vertex has at least as many chips as neighbors we can "fire" it by sending each neighbor a chip.

(Wee Kean here.)

(Yu Peng here) I'll be going through a pretty cool concept in graph theory: flows! I'll start off by explaining what a flow network is, then go on to demonstrate how we can make use of flows to easily prove some theorems in graph theory, for example, Hall's Marriage Theorem. Finally, we'll look at an olympiad problem.

(David here!) I wanted to talk about a problem I encountered in 2020 during Putnam seminar, and the subsequent exploration I did on it. It's still unresolved but I hope my thought processes could help those who are interested in understanding how to propose problems.

Hi everyone! Sheldon here. I've been working for a while, so I haven't had many opportunities to do Olympiad math recently (or at college, for that matter). However, a few days ago, some of my friends and I had the privilege to attend an event where we met some students who had gone to this year's IMO.