Social (in)justice is a key issue in today’s cities, which are characterized by growing socio-economic inequalities. Divided cities—such as Jerusalem and Nicosia—experience further tensions in light of their unstable geopolitical condition. While divided cities have been studied from a number of angles, little is known of the daily challenges that divided communities experience at the neighbourhood scale. This research proposes to study divided communities in East Jerusalem to examine the pressures that they experience and to elucidate the strategies they employ to better off their lives. Situated in the realm of urban planning, the study focuses on four key issues: a) governance, b) local leadership), c) housing, and d) municipal services, infrastructure and public space. The project utilizes diverse methods including interviews, focus groups, on-site visits, and mental maps to study the dynamics of integration and exclusion in three Palestinian and Israeli-Palestinian East Jerusalem neighbourhoods. This project involves an Advisory Board composed of experts in the fields of urban studies and political science, providing scholarly expertise and access to the research area. The project will be disseminated through scholarly publications and conference presentations. Moreover, a public outreach programme has also been designed to communicate the findings to local communities, NGOs, and policy makers. In addition, local Palestinian students will be participate in research activities. The project will advance the training of the Fellow, enabling her to reach a position of independence through learning new methods, mentoring students, and leading the planning and execution of the project. Findings from the research would extend beyond the particular status of divided cities, contributing to a more inclusionary planning theorization and practice by applying lessons from the experience of marginalized communities in Jerusalem to marginalized communities elsewhere.

I will expand the experimental reach of tunneling spectroscopy to new materials and device geometries. The technique is ideal for tackling two challenges: (i) Probing Andreev bound states and Majorana states in graphene and topological insulators (TIs) coupled to superconductors, and (ii) realizing momentum-conserving tunneling. I will utilize a breakthrough in device fabrication to stack layered van-der-Waals materials, such as graphene and hexagonal Boron Nitride (hBN), to form vertical structures. Ultrathin layers of mechanically deposited dielectrics will be used as tunnel-barriers. These can interface any smooth surface, expanding the range of possible device-based tunneling systems. A tunnel junction has decisive advantages over STM in access to lower temperatures and hence higher energy resolution. Significantly, the effort to probe the energy spectra of graphene and TIs coupled to superconductors is often resolution-limited. I will develop artificial-vortex devices and Josephson devices where induced spectra are expected to reveal the Majorana mode, a quantum state of unusual statistics sought as a platform for fault-tolerant quantum computation. Using the same technology, I will develop devices where tunneling takes place between extended states. The aim is to realize momentum resolved tunneling for μeV-resolution measurement of dispersions in graphene, other 2D systems, and smooth interfaces. Momentum control will be achieved using density-tuning of the Fermi surfaces or using parallel magnetic field. The high resolution spectra will reveal details of interaction effects, manifest as modifications to the single-electron picture. Carriers can be injected into a system with full control over their direction and energy – a powerful experimental knob, useful for injecting carriers using one electrode and extracting them in another. Such geometry is sensitive to relaxation effects, and will allow unprecedented resolution studies of out-of-equilibrium systems.

Modern data analysis and optimization rely on our ability to process rapidly evolving dynamic datasets, often involving matrix operations in very high dimensions. Dynamic data structures enable fast information-retrieval on these huge databases by maintain- ing implicit information on the underlying data. As such, understanding the power and limitations of dynamic (matrix) data structures is a fundamental question in theory and practice. Despite decades of research, there are still very basic dynamic problems whose complexity is (exponen- tially) far from understood – Bridging this gap is one of the centerpieces of this proposal. The second theme of this proposal is advancing the nascent role of dynamic data structures in continuous optimization. For over a century, the traditional focus of optimization research was on minimizing the rate of convergence of local-search methods. The last ∼3 years have witnessed the dramatic potential of dynamic data structures in reducing the cost-per-iteration of (Newton type) optimization algorithms, proclaiming that the bottleneck to accelerating literally thousands of algorithms, is efficient maintenance of dynamic matrix functions. This new framework is only at its early stages, but already led to breakthroughs on decade-old problems in computer science. This proposal will substantially develop this interdisciplinary theory, and identifies the mathematical machinery which would lead to ultra-fast first and second-order convex optimization. In the non-convex setting, this proposal demonstrates the game-changing potential of dynamic data structures and algebraic sketching techniques in achieving scalable training and inference of deep neural networks, a major challenge of modern AI. Our program is based on a novel connection of Kernel methods and compressed sensing techniques for approximate matrix multiplication.