[20190315 : Colloquium]From Diophantine equations to Elliptic curves
5. 초록:
In the history of number theory, the Fermat's Last Theorem, proven by Andrew Wiles and Richard Taylor, is one of the deep and beautiful results, in
which, at least two seemingly unrelated mathematical areas were used in its proof.
Roughly speaking, the theorem was proved by relating the existence of integer solutions of certain Diophantine equations to a special property, called modularity,
of the corresponding elliptic curves. This kind of phenomenon occurs many times in various fields of math to reveal the beauty of mathematics.
In the first half of the talk, as a motivating example, we briefly review the Fermat's Last Theorem to illustrate this phenomenon. Afterwards, I will introduce
one of my own results on the automorphism groups of polarized abelian surfaces over finite fields, which is similar to Fermat's Last Theorem in the sense of
this phenomenon, where we need to use 5 different mathematical areas to achieve it