Lectures on modular curves

Hwajong Yoo (SNU)

February 7 (Thurs)   2019, 13:00~14:30, 15:00~16:30 하나스퀘어 119호 (하나스퀘어 위치)

AbstractIn the first talk, we will study the theory of modular curves over the field of complex numbers. consists of two parts:
1. the theory of elliptic curves over the field of complex numbers.
2. the theory of compact Riemann surfaces and their Jacobian varieties.
We will review relevant results and give heuristic explanation of the theory instead of giving rigorous proofs of well-known theorems.

In the second talk, we will focus on the theory of modular curves over the field of rational numbers. We will deal with the following.
1. Constructing Galois representations attached to cuspidal eigenforms of weight 2.
2. Constructing rational torsion points on the Jacobian varieties of modular curves.