Ion implantation engineered photonic devices for use in highly integrated silicon optoelectronic circuits. This project establishes a collaboration with Canada's leading integrated silicon photonics research group thus tapping into years of valuable experience transferable to Australian-based researchers. The involvement of students as well as early career researchers ensures a new generation of Australian experts in this field. The importance of silicon photonics means that Australia must estab ....Ion implantation engineered photonic devices for use in highly integrated silicon optoelectronic circuits. This project establishes a collaboration with Canada's leading integrated silicon photonics research group thus tapping into years of valuable experience transferable to Australian-based researchers. The involvement of students as well as early career researchers ensures a new generation of Australian experts in this field. The importance of silicon photonics means that Australia must establish a strong research program in the area to maintain its current position as being at the forefront of leading-edge research. This is only possible through collaborations such as that proposed here.Read moreRead less
Propagation of singularities for the Schrodinger equation. The time-dependent Schrodinger equation governs the evolution of quantum particles. In this project we aim to use new techniques from mathematical scattering theory to analyse solutions of the Schrodinger equation and obtain sharp bounds on their singularities. Controlling such singularities will allow us to deduce quantitative bounds on the number of eigenvalues in certain situations, and provide new techniques for studying nonlinear Sc ....Propagation of singularities for the Schrodinger equation. The time-dependent Schrodinger equation governs the evolution of quantum particles. In this project we aim to use new techniques from mathematical scattering theory to analyse solutions of the Schrodinger equation and obtain sharp bounds on their singularities. Controlling such singularities will allow us to deduce quantitative bounds on the number of eigenvalues in certain situations, and provide new techniques for studying nonlinear Schrodinger equations. Read moreRead less
Asymptotic Geometric Analysis and Machine Learning. Phenomena in large dimensions appear in a number of domains of Mathematics and adjacent domains of science (e.g. Computer Science), dealing with functions of infinitely growing number of parameters. Here, we focus on several questions naturally linked to Asymptotic Geometric Analysis which have natural applications to Statistical Learning Theory. We intend to use geometric, probabilistic and combinatorial methods to investigate these problems, ....Asymptotic Geometric Analysis and Machine Learning. Phenomena in large dimensions appear in a number of domains of Mathematics and adjacent domains of science (e.g. Computer Science), dealing with functions of infinitely growing number of parameters. Here, we focus on several questions naturally linked to Asymptotic Geometric Analysis which have natural applications to Statistical Learning Theory. We intend to use geometric, probabilistic and combinatorial methods to investigate these problems, with an emphasis on modern tools in Empirical Processes Theory and the theory of Random Matrices.Read moreRead less