Noncommutative geometry of groups acting on buildings. Consider a tiling of the plane by triangles, where each triangle is labeled by an element of a finite alphabet. Suppose that only certain pairs of labels are allowed to be adjacent to each other in each direction. The tiled planes can be pasted together to form the abstract mathematical object known as a building. This building and its boundary, give rise to new families of C*-algebras and groups. The algebras have a rich structure which it ....Noncommutative geometry of groups acting on buildings. Consider a tiling of the plane by triangles, where each triangle is labeled by an element of a finite alphabet. Suppose that only certain pairs of labels are allowed to be adjacent to each other in each direction. The tiled planes can be pasted together to form the abstract mathematical object known as a building. This building and its boundary, give rise to new families of C*-algebras and groups. The algebras have a rich structure which it is proposed to investigate and link with geometric properties of the groups. New insights into geometry, dynamics and algebra are expected.Read moreRead less
Categorical splitting theorems in algebraic geometry. Algebraic geometry is the study of solutions of polynomial equations.
It is one of the richest fields of Mathematics, and has led to advances in cryptography and other areas of technology. The project aims to apply in this field some recently developed abstract techniques in order to obtain results of a new type. It is also expected that the approach taken will help to simplify and unify the
branches of algebraic geometry considered. Proje ....Categorical splitting theorems in algebraic geometry. Algebraic geometry is the study of solutions of polynomial equations.
It is one of the richest fields of Mathematics, and has led to advances in cryptography and other areas of technology. The project aims to apply in this field some recently developed abstract techniques in order to obtain results of a new type. It is also expected that the approach taken will help to simplify and unify the
branches of algebraic geometry considered. Projects of a theoretical
nature such as this one help to maintain Australia's high standing in
the international scientific community.Read moreRead less