The aim of this project is to gather mathematicians working in complex and algebraic geometry on the one hand and in geometric group theory and topology on the other hand. The interactions between these fields are fruitful, have a long history and have seen remarkable recent developments. The members of this project are united by a common interest for group theory and almost all of them have already worked on topics related to fundamental groups of kähler and algebraic varieties or groups of automorphisms and of birational transformations of algebraic varieties. We aim at developing a common background in geometric group theory, complex differential geometry and algebraic geometry. We plan to organize a yearly workshop to gather the members of the project, as well as their phd students. Doctoral training will be a key element of the project. We also wish to hire postdoctoral researchers, to foster collaborations between members of the group and to organize one international conference at the end of the project. Among other things, we plan to approach the following research topics: (1) the study of group of birational transformations in arbitrary dimension, notably via their action on nonpositively curved spaces, the study of birational structures on algebraic varieties. (2) the study of the Kodaira problem for the fundamental group, and its link with the minimal model program in the kähler context. (3) the study of complex hyperbolic lattices, as well as the study of toroidal compactifications of finite-volume noncompact quotients of the unit ball of C^n. This family of examples combines a large part of the research topics of the members of this project (complex hyperbolicity, small cancellation theory in geometric group theory, finiteness properties of groups).

Biodiversity loss in conventional farmland is one of the most pressing issues that humanity has to face. Using the approach of living labs that promote the involvement of citizens in science, this project strives to collectively develop field-to landscape management, mainly by floral enrichment, and bioindicators about the conservation state of farmland biodiversity. In this project, we will focus on cereal fields along a climatic gradient from the mild Atlantic climate (western France) to the more continental climate of central Europe (western Czech Republic). In line with the concept of ecological intensification, conservation of biodiversity aims at maximizing ecosystem services, here pest and weed controls and pollination, and to minimize disservices (presence of weeds and pests, loss of crop yields). The European climatic scale investigated will help to provide European-wide solutions for adaptation to land-use and climate changes. Along a climatic gradient, it is expected that the climatic context plays a major role on the potential of ecosystem services in each area. Therefore, to be able to effectively design plant floral enrichment that supports pest and weed control as well as pollination at the European scale, a study is needed on a large spatial and climatic gradient that would include a large range of taxa (wild flowers, slugs, aphids, parasitoids, hyperparasitoids, spiders, rove beetles, carabids, dung beetles, syrphids, butterflies, and bees) and landscape contexts. Simultaneously managing multiple ecosystem services requires understanding the mechanisms underlying ecosystem service interactions. The approach we propose to tackle this problem is multidisciplinary and based on the combination of the living lab concept, citizen-based means of field data collection called BioBlitz, and manipulated field experiments by floral enrichment that will reflect the results of the living lab, BioBlitz and scientific data. Among the outcomes of the project, living labs will be established in the four countries involved (France, Belgium, Germany and Czech Republic). To assess biodiversity, we will develop two kinds of multi-taxon-based integrated indicators. Finally, scenarios of adding diversity within, nearby and in the surroundings of the fields in order to optimize diversity in agro-ecosystems at the farm/landscape scales will be co-developed in living labs with farmers to engage them, in protecting biodiversity and ecosystem health. Our approach will contribute to the knowledge needs specified in the Themes 1 and 2 of the Call document Biodiversa+. Our project will provide tools adapted to different climatic/and local to landscape practices as the chosen countries are contrasted in their climate, landscape history and agricultural practices. The consortium includes 5 academic partners, a company and 2 stakeholders, that will ensure the dissemination of the results to the farmers.