Vortrag
What is... an adelic torus orbit?
Vortrag von Konstantin Andritsch
Datum: 30.04.24 Zeit: 16.30 - 17.30 Raum:
''As the term suggests - Adelic torus orbits - are nothing but the orbit of an algebraic torus over the ring of Adeles. They provide a powerful tool to collectively study the behavior of collections of geometric data given by arithmetic data. In this talk we will motivate the use of adelic torus orbits by looking at a concrete example: > Already in the 19th century Gauss studied integral binary quadratic forms. He observed that there are essentially only finitely many different integral binary quadratic forms with fixed discriminant. In more modern terms, these different forms arise through a natural action of the ideal class group of a quadratic number field. To study the properties of different forms at the same time it is convenient to consider the Adelic extension of the modular curve. We will see that forms who are not equivalent over the integers might be equivalent over the Adeles. After introducing the necessary concepts and motivating the idea behind Adelic torus orbits we will discuss how they can be used to prove equidistribution results on (real) homogeneous spaces.''