About

My name is Koopa Koo, and I am a number theorist. In particular, my research interests include: Iwasawa theory for Big Representations, Galois Representations, Elliptic Curves, Modular Forms, Iwasawa Invariants attached to -adic representations, and combinatorial algebraic additive number theory.

So what is number theory?

I will give a quote be Hida:

“Traditionally, mathematical research has been classified by the method mathematicians exploit to study their research areas, except possibly for number theory. For example, algebraists study mathematical questions related to abstract algebraic system in a purely algebraic way (only allowing axioms defining their algebraic systems), differential geometers study manifolds via infinitesimal analysis, and algebraic geometers study geometry of algebraic varieties (and its siblings) via commutative algebra and category theory. There are no central techniques which distinguish number theory from other subjects, or rather, number theorists exploit any techniques available to hand to solve problems specific to number theory. In this sense, number theory is a discipline in mathematics which cannot be classified by methodology from the above traditional viewpoint but is just a web of rather specific problems (or conjectures) tightly and subtly knit to each other. We just study numbers, those simple ones, like integers, rational numbers, algebraic numbers, real and complex numbers and -adic numbers, and that is it.”

I like this quote a lot because it’s perhaps the most accurate description of number theory I have seen. (according to my understanding)

I started this blog to share mathematics that I find interesting, and to share my teaching philosophy and some problems I propose for various purposes. My intended audience are NOT the experts in my research fields, but rather my students, especially my students in IMO training, and the students in various courses that I teach at universities.

In my blog, you will find various problems I proposed for the selecting the IMO team members representing Hong Kong, and the background of each problem. Some selected problems in public examinations in Hong Kong in which I would share “unconventional” solutions that is often shorter or easier than the intended solution. Various articles for promoting interests in number theory and mathematics in general.

Thank you for reading and let’s see some math!