Number theory is a very attractive subject to study because some of its problems are so easy to understand but hard to solve, such as Fermat’s Last Theorem and ABC conjecture, and others give deep connections between two totally different objects such as BSD conjecture. Moreover, you can try any tools you can imagine, e.g. algebraic geometry/arithmmetic geometry, representation theory, analysis, probability, and PDE. In last fifty years, we also see applications of number theory to Cryptosystem and others. In this talk, I will informally talk about some of my personal experience with Gross-Zagier- Zhang formula, and its degenerate case—factorization of norm of CM values of modular functions. The latter led me to some of interesting application to Cryptography.
