Mathematics Commons^™

Numerical Studies Of Correlated Topological Systems, Rahul Soni

Doctoral Dissertations

In this thesis, we study the interplay of Hubbard U correlation and topological effects in two different bipartite lattices: the dice and the Lieb lattices. Both these lattices are unique as they contain a flat energy band at E = 0, even in the absence of Coulombic interaction. When interactions are introduced both these lattices display an unexpected multitude of topological phases in our U -λ phase diagram, where λ is the spin-orbit coupling strength. We also study ribbons of the dice lattice and observed that they qualitative display all properties of their two-dimensional counterpart. This includes flat bands near …

A Coarse Approach To The Freudenthal Compactification And Ends Of Groups, Hussain S. Rashed

Doctoral Dissertations

The main purpose of this work is to present a coarse counterpart to the Freudenthal compactification and its corona (the space of ends) that generalizes the Freudenthal compactification of a Freudenthal topological space X (connected, locally connected, locally compact and σ-compact) and its corona; then applying it to groups as coarse space to obtain generalizations to many well-known results in the theory of ends of groups. To this end, we present two constructions:

1. The Coarse Freudenthal compactification of a proper metric space which is a coarse compactification that coincides with the Freudenthal compactification when the metric space is geodesic. …