# Akihiko YUKIE

- Name
- Akihiko YUKIE
- Title
- professor
- yukie (please add
`@math.kyoto-u.ac.jp`

) - URL
- http://www.math.kyoto-u.ac.jp/~yukie
- Research Area
- Number Theory
- Profile
■ Research area

Automorphic forms，geometric invariant theory■ Research topics

An algebraic group is a group whose operation is described by polynomials. For example, the group of n by n non-singular matrices is an algebraic group called the general linear group. If you consider algebraic groups over the field of rational numbers, one can consider various number theoretic questions. Research area of this kind is called "the number theory of algebraic groups." The theory of quadratic forms is classical in number theory. Since the general linear group is acting on the space of quadratic forms, it is deeply related to the theory of algebraic groups. Whether or not two quadratic forms are equivalent over the field of rational numbers is a typical problem in number theory of algebraic groups. In number theory of algebraic groups, analytic method is often used and the theory of automorphic forms is a part of it. I am doing research mainly on a thing called "prehomogeneous vector spaces." I am interested in density theorems related to algebraic groups.