Events

Extracting the square root of a number and its reciprocal play fundamental role in 3D graphics (e.g. normalizing vectors). In this talk, we will discuss the fast (and brilliant) inverse square root algorithm from the game Quake III and analyze its performance.

More information: https://zucmap.ethz.ch/call_made

The notion of a John domain was initially introduced in 1961 by Fritz John, and later named after him by Martio and Sarvas. Typically, its study is motivated by its connections to the properties of quasiconformal and quasisymmetric mappings. Moreover, John domains find extensive applications in the theory of Sobolev functions in metric measure spaces and functional analysis, as they represent essentially the sole class of domains that uphold the Sobolev-Poincaré inequality. In this presentation, I will introduce several recent applications of John domains in the theory of the calculus of variations.

''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.