For centuries, mathematical concepts have inspired technological progress. As the distance between fundamental research and applications shortens, the impact of mathematics on our everyday lives becomes stronger, and the long-standing European tradition of excellence in mathematical research reaffirms itself as a key factor of sustainable economic growth. In line with that tradition, the goal of the present project is to achieve and disseminate high-impact research results in the field of Differential Geometry, that will irrigate related disciplines, such as Theoretical Physics and, in the longer run, more applied fields. The applicant’s outstanding research record in Gauge Theory and Representations of Fuchsian Groups, combined with the expertise of his European hosts in the rapidly growing area known as Higher Teichmüller Theory, make the proposed collaboration between them unique, timely, and ideally shaped for success. The research results that they are setting out to obtain will redefine the field and open new lines of research. Moreover, the host institution is committed to providing high-quality training of the applicant at every step of the action, from concrete initiatives to reduce the gender gap in mathematical sciences to the use of technological tools for the dissemination and communication of research results. The completion of the present research project will thus bring a significant boost to the applicant’s career and establish the host institution as a pioneer in a new line of research, hereby strengthening its tradition of excellence and innovation. The project is in accordance with the recommendations of the 2016 consultation of the European Commission for Mathematics in Europe, according to which “the wealth of mathematical competence in Europe and its potential for European science and industry is undeniable”.

Rapidly expanding field of cancer diagnostics generates strong demand for new biosensing tools. In particular, it concerns probes for fluorescence in situ hybridization (FISH), that enables detection of DNA and RNA cancer biomarkers directly in diseased cells. Although FISH technique has already been accepted for cancer diagnostics in clinics, its applications are still limited because the method is slow, expensive and requires complicated amplification protocols to obtain sufficient fluorescence signal. Here, we propose a solution based on ultrabright DNA-functionalized dye-loaded fluorescent polymeric nanoparticles recently developed within the ERC grant BrightSens and protected by two patent applications. We aim to develop ultrabright FISH probes (nanoprobes) for cancer research and clinical diagnostics. These nanoprobes will feature single-molecule DNA/RNA sensitivity, low cost, fast and direct one step cell staining protocol, and compatibility with clinical samples and single-cell assays. The amplification of FISH performance will be ensured by our dye-loaded polymeric nanoparticles of 7-20 nm size that are ~1000 fold brighter than single organic dyes. The project is composed of five tasks: (1) Synthesis and optimization of FISH nanoprobes; (2) validation of FISH nanoprobes in cancer cell lines; (3) development of multiplexing assays for detection at least 9 biomarkers; (4) their validation in clinically relevant samples; and, finally, (5) commercialization of FISH nanoprobes. The developed probes will constitute highly competitive products that can greatly improve performance of FISH assays in clinics and research laboratories and thus impact human health. Therefore, they will be directly proposed for commercialization by licensing to existing companies and/or through creation of a startup.