Members

In number theory, we study phenomena arising from integers. Among many directions in modern number theory, I am interested in the conjectural Langlands correspondence. In mathematics, we can often find a mysterious relationship between two completely different objects. We can say that the Langlands correspondence is one of the most important conjectures which predict such a kind of mysterious relationship in number theory. If we believe this conjecture, we can find a lot of unknown phenomena, which are called the Langlands functorialities. In my study in the Hakubi project, I will try to prove those Langlands functorialities by using harmonic analysis, which is a theory of investigating functions on groups. The point here is that this approach is logically independent of the conjectural Langlands correspondence. Thus I hope this study will eventually lead us to establish the Langlands correspondence by using the Langlands functoriality conversely.