Eversince, the study of symmetry in mathematics and mathematical physics has been fundamental to a thourough understanding of most of the fundamental notions. Group theory in all its forms is the theory of symmetry and thus an indispensible tool in many of the basic theoretical sciences. The study of infinite symmetry groups is especially challenging, since most of the tools from the sophisticated theory of finite groups break down and new global methods of study have to be found. In that respect, the interaction of group theory and the study of group rings with methods from ring theory, probability, Riemannian geometry, functional analyis, and the theory of dynamical systems has been extremely fruitful in a variety of situations. In this proposal, I want to extend this line of approach and introduce novel approaches to longstanding and fundamental problems. There are four main interacting themes that I want to pursue: (i) Groups and their study using ergodic theory of group actions (ii) Approximation theorems for totally disconnected groups (iii) Kaplansky’s Direct Finiteness Conjecture and p-adic analysis (iv) Kervaire-Laudenbach Conjecture and topological methods in combinatorial group theory The theory of `2-homology and `2-torsion of groups has provided a fruitful context to study global properties of infinite groups. The relationship of these homological invariants with ergodic theory of group actions will be part of the content of Part (i). In Part (ii) we seek for generalizations of `2-methods to a context of locally compact groups and study the asymptotic invariants of sequences of lattices (or more generally invariant random subgroups). Part (iii) tries to lay the foundation of a padic analogue of the `2-theory, where we study novel aspects of p-adic functional analysis which help to clarify the approximation properties of (Z/pZ)-Betti numbers. Finally, in Part (iv), we try to attack various longstanding combinatorial problems in group theory with tools from algebraic topology and p-local homotopy theory.

Modern technology should not only provide improved efficiency but follow sustainable and minimalistic design principles for an optimised ecological footprint. Photonic applications, e.g., used for information processing in logistics or sensor systems, currently require more and more complex technological solutions to speed up data storage and processing while creating nonrecyclable waste. SLOWTONICS aims at providing a paradigm shift based on biocompatible organic optoelectronic and photonic components. The design principle of digital luminescence developed in my research group combines easily processable excitonic states at long lifetimes (> 1 µs) with a programmable oxygen-based switch of the luminescence to create a unique programmable photonic framework. By using organic semiconductors, such systems offer a low ecological footprint, small material consumption, and a high degree of material tuneability for tailor-made technological solutions. First prototypes of programmable luminescent tags have demonstrated the potential of this technology yet missing the requirements for industrial application. Based on the existing expertise of my research group in the fields of organic optoelectronics and spectroscopy of soft luminescence materials, SLOWTONICS will overcome current limitations, to realize industry-relevant systems for optical data storage and exchange, and extend the application of digital luminescence towards luminescent security label and multi-component sensor systems. Once having developed novel communication components, we attempt to realize these designs made only from materials found in nature. This is an essential ultimate step because a world with an ever-growing demand for information requires systems that provide functionality and allow for responsible use. Our approach aims at systems that have material footprints of < 0.1 mg/system, making them truly minimalistic and sustainable.

The HoMe (Historical Grounding of Migration Decisions of People at Environmental Risks) project will provide insights on historical reasons of migration decisions (to migrate or to not migrate) of people at environmental risks. Current research on environmental migration claims that mostly the poor are migrating due to disaster. However, motivations of environmental non-migration go beyond resources constraints and are understudied and not yet understood as migration decisions. The factors contributing to non-migration are supposed to be not simply the inverse of those that motivate to migrate. Rather it is assumed, non-migration is also influenced by the settlement history of a community. Going beyond the state-of-the-art, this project will develop for the first time an analytical framework using Ostrom’s socio-ecological system framework for examining the historical grounding of migration decisions. Second, it will model how changes of the social, political and environmental conditions over time influence migration decisions using agent-based modelling. Third, the model will be used to explore possible future migration decisions based on alternative scenarios of changing societal and environmental conditions in the future making use of the findings from the influence of the historical grounding. This novel and timely study will significantly advance scientific knowledge on environmental migration and the respective modelling capabilities, particularly in the emerging field of 'Environmental Non-Migration'. Results will provide a major contribution to global adaptation policy frameworks, including the SDGs and the EU’s Agenda on Migration. The realisation of this cutting-edge project will substantially support the applicant to achieve higher level of professional maturity. It will be hosted by two excellent, highly experienced and internationally renowned institutes: University of Colorado Boulder (outbound) and Technische Universität Dresden (inbound).

The continuous progress of persistent room-temperature phosphorescence (p-RTP) emitting in near infrared (NIR) with high potential for long-lifetime and flexible optoelectronic applications is spearheaded by the development of novel materials. Much of this interest is also due to the concomitant advantages of the organic light-emitting diode (OLED) technology. Future OLED displays are envisioned to comprise an additional NIR pixel for imaging and security protocols. Equally such NIR OLEDs can be used as a monolithically manufactured light sources in bioimaging applications. However, limited by the energy gap law, the majority of p-RTP materials emit in the visible region, NIR phosphors are rarely reported. To solve this challenge, this project aims to progress along two clear research directions: i) engineering efficient NIR p-RTP emissive material systems and ii) developing well-performing (persistent) NIR OLEDs. To construct NIR p-RTP material systems, we will put in action work packages (WPs) 1-2 by employing available organic materials to engineer host/guest emissive systems with high efficiency and stability. The correlation of their photophysical properties to the molecular microenvironment will also be investigated using the state-of-the-art spectroscopy methodologies to elucidate the mechanisms. WPs 3-4 will use established OLED fabrication routines to develop efficient NIR down-conversion OLED pixels with persistent emission and transfer the knowledge to an industrial R&D environment. The multi-disciplinary project will bridge the gap between the fundamental material research of NIR p-RTP emission and the monolithic integration of these systems in actual OLEDs as down-conversion layers for advanced sensing applications through joint research in physics, engineering and material science. I can perfectly bring in my existing skills, further broaden my expertise substantially and foster academic and industrial connections to build my future career network.