Nanostructures drive the world around us. Every modern electronic device contains integrated circuits and nano-electronics to provide its functionality. Advances in nanotechnology directly impact society by enabling smartphones, autonomous devices, the internet of things, data storage, and essentially all forms of advanced technology. Fabricating such nanostructures crucially depends on having the tools to make them visible without destroying them. Modern nanodevices often have complex three-dimensional architectures with small features in all dimensions. While imaging methods that achieve nanometer-scale resolution exist, there are currently no compact tools that can look inside 3D nanostructures made out of metals and semiconductors without damaging their delicate internal structure. I will address this challenge by developing compact tools to image 3D nanostructures in a non-invasive way. Even though most nanostructures are completely opaque to visible light, I will develop light-based methods, combined with computational imaging techniques developed in my previous ERC project, to look inside them with unprecedented resolution and contrast. Light-based imaging is unparalleled in speed and versatility, and allows contact-free detection. My proposal is to: 1) Use compact laser-produced soft-X-ray sources to image nanostructures with high 3D resolution and element-sensitive contrast; 2) Use laser-induced ultrasound pulses to image complex 3D nanostructures, even through strongly absorbing materials; 3) Employ computational imaging methods to reconstruct high-resolution 3D object images from the resulting complex diffraction signals. I will forge a coordinated research program to bring these concepts to reality. This program provides exciting prospects for fundamental science and industrial metrology. I will go beyond the state-of-the-art in nano-imaging, to extend our vision into the complex interior of the smallest structures found in science and technology.

Integer programming (IP), i.e. linear optimization with integrality constraints on variables, is one of the most successful methods for solving large scale optimization problems in practice. While many of the base IP problems such as the traveling salesman problem (TSP) or satisfiability (SAT) are NP-Complete, IPs with tens of thousands of variables are routinely solved in just a few hours by current state of the art IP solvers. The main goal of this proposal is to develop a quantitative theory capable of explaining when and how well different IP solver techniques will work on a wide range of instances. Here we will study many of the principal tools used to solve IPs including branch & bound, the simplex method, cutting planes and rounding heuristics. Our first direction of study will be to develop parametrized classes of instances, inspired by the structure of realistic models, on which branch & bound and the simplex method are provably efficient. The second research direction will be to develop alternatives to ad hoc rounding heuristics and cutting plane selection strategies with provable guarantees and provide their applications to important classes of IPs. Lastly, we will explore the power and limitations of IP techniques in the context of algorithm design by comparing them to powerful techniques in theoretical computer science and analyzing their worst-case performance for solving general integer programs. While the main thrust of this proposal is theoretical, it will be complimented by an experimental component performed in collaboration with well-known experts in computational IP, both to gain valuable insights on the structure of real-world instances and to validate the effectiveness newly suggested approaches. The proposed research is designed to make breakthroughs in our quantitative understanding of IP techniques, many of which have long resisted theoretical analysis.

The main goal of EXPLEIN is to unravel the limiting factors in the charge carrier transport in perovskite thin films, stacks, and solar cells, aiming to pre-select suitable material compositions for and optimisation of light-converting devices. First, I will gain deep understanding of the role of grain boundaries – typically limiting charge carrier diffusion due to an increased number of recombination centres – in thin films and lamellae, which I will then apply to interfaces in stacks and devices, ultimately allowing me to monitor and improve the performance of perovskite-based solar cells. The centre piece of this work is a scanning electron microscope equipped with cathodoluminescence (CL) and pulsed electron beam capabilities. I will expand those with electrical sample biasing for operando conditions and develop a novel light in-coupling module. This unique, versatile method will facilitate local injection of electrons and photons into the same sample area, thereby allowing for the in-depth study of the differences in morphology (via in-situ secondary electron imaging), optical (via CL and CL lifetimes) and electrical properties upon selective sub-bandgap-energy illumination, applied electrical bias, and local e-beam placement. The diffusion length, a key parameter for solar cell absorbers, will be measured directly and via CL-lifetimes which I will subsequently link to the sample’s average grain size of various perovskite compositions. The perovskite database will serve as platform for comparison and exchange of knowledge, ultimately allowing to advance and expand the research field. The multitude of the proposed experiments will allow me to gain new and detailed insights into the micro- and nanoscopic charge carrier transport in several types of perovskites, giving me the opportunity to contribute to the advancement of solar cells necessary for the challenging transition to cost-effective and sustainable energy.

Codes and lattices are two major mathematical platforms to build quantum-resistant cryptosystems. Theose cryptosystems will soon be standardized and deployed, replacing historical solutions threatened by Shor's quantum algorithm. These new cryptosystems rely on the hardness of finding short vectors in a code or in a lattice, a computational problem called reduction. Our confidence in their security relies on the relentless effort of cryptanalysis: quantifying, elucidating and trying to invalidate such hardness assumptions. *My ERC project aims at discovering faster cryptanalytic algorithms and at building better cryptography via the development of a unified reduction theory enabling a systematic transfer of techniques between codes and lattices.* As an underpinning example for this project, I have successfully transferred the seminal LLL reduction algorithm to binary codes, an algorithm still playing a central role in the cryptanalysis of lattices. This unified theory will also lead to better mathematical and algorithmic abstractions, improve the clarity, generality, and composability of known techniques. Such qualitative enhancements will also help to obtain quantitative ones. In turn, I will implement these enhancements into open-source libraries, designed for either high-performance or ease-of-use, in order to stimulate further algorithmic exploration by the community. Beyond algorithms, my approach will also create new connections between existing mathematical theories and the hardness of code and lattice problems. For instance, it leads to consider moduli spaces as a new powerful tool for proving average-case hardness. By its contributions to both the theoretical and practical aspects of the hardness of lattice and code problems, this project will play a key role in the ongoing transition to quantum-resistant cryptography.

Friction contributes to the global computer chip shortage: friction and wear limit the positioning accuracy and throughput in chip production. As future positioning requirements approach the atomic scale, contact, friction and wear need to be understood at this scale to inspire new positioning solutions which are more urgently needed than ever before. CHIPFRICTION will focus on a key interface in chip production: carbon based material-on-silicon subjected to nanoslip in a hydrogen-rich environment. How nanoscale elasticity, plasticity and adhesion control rough contact formation will be revealed by matching contact models to ground-breaking fluorescence microscopy contact observations. How a local frictional stability criterion translates into the nanometre partial slip that characterizes the onset of multi-contact sliding will be modelled and observed through unique pre-sliding experiments. The oxidation, interfacial bonding and mechanical mechanisms that lead to wear of the carbon based material will be exposed through a combination of environmental control, new nanowear visualization methods and ex-situ XPS characterization. I am uniquely suited to conduct this work because I have fuelled the development of these experimental techniques, and I have experience in conducting the associated physical modelling. Macroscopic friction emerges from generic physical ingredients such as elastic deformation of surface topography and shearing of interfacial covalent bonds. How friction emerges, creates a scientific challenge with major impact: Friction is responsible for 25% of the world's energy consumption. I will address this long-standing challenge by experimenting and modelling the complex interplay between contact mechanics, frictional slip and wear of the specific interface. The transfer of new friction manipulation strategies for chip production without friction is facilitated by having an institutional link to the lithography industry.