Luxembourg National Research Fund

The FNR is pleased to communicate the results of the 2021 OPEN Call for proposals: 3 of 9 eligible projects have been retained for funding, an FNR commitment of 1.3 MEUR. 

The OPEN programme provides funding for a limited number of high quality research projects in areas that are currently not covered by the FNR’s thematic CORE programme. It aims at supporting established researchers to pursue innovative research projects of high scientific quality in emerging research areas in Luxembourg. In order to identify the most excellent projects, the FNR submits project proposals to an assessment by independent international experts. Among the 6 project proposals that were submitted, 2 have been selected for funding.

Go to OPEN programme page

Funded projects

Abstract

The discovery of the hyperbolic plane in the 19th century was an eye opening moment in mathematics, and lead to new perspectives in geometry and analysis, but also to the development of topology. Ever since, it has remained an object of extraordinary fascination, and through mathematical popularization, the work of math historians and artists such as Escher, it has become one of the rare sophisticated geometric objects to be known outside the world of mathematics. Hilbert famously proved that it could not be “smoothly” embedded – or even immersed – isometrically into Euclidean space, which probably added to its reputation as being abstract and mysterious, at least for the general public, as this is sometimes translated as “it cannot be seen” in Euclidean space. More generally, hyperbolic surfaces (that is surfaces that locally look like the hyperbolic plane) play a ubiquitous role in mathematics, providing links between radically different areas of study such as number theory, dynamics, and geometric topology. Associated to these surfaces are moduli spaces, which encode all possible geometries a given topological surface can have. McShane type identities are collections of equalities involving lengths of geodesics, and were famously used by Mirzakhani to compute volumes of moduli spaces.

In this project, we aim to further the understanding of hyperbolic surfaces in two main directions, both on the common theme of visualization. The first is to obtain the first visualization of an isometric copy of the hyperbolic plane in Euclidean space, the existence of which was famously proved by Nash and Kuiper in the 1950s. The second is to provide visualizations of the McShane-Mirzkahani identities by exhibiting imagery of the associated fractal decomposition of the boundary of a hyperbolic surface.

Abstract

Cannabis sativa is rightfully named “the plant of the thousand and one molecules” because of the rich diversity of its phytochemicals. Its molecules are used in several fields, spanning pharmaceutics, cosmetics, nutraceutics, in light of their documented bioactivities. For example, Cannabis phenolic compounds have antioxidant and antimicrobial properties which are useful for the manufacture of nutraceuticals, cosmeceuticals and bactericidal products. The abundance of such compounds depends both on intrinsic genetic characters (as for example those found in different varieties or accessions) and on environmental conditions (such as the presence of exogenous stresses during the growth of the plants). In the project, twenty-one accessions of C. sativa from different geographic locations will be screened to find those that produce the highest amounts of phenolic compounds and they will be stimulated using mild salinity. Low doses of salt stress are known to stimulate plant growth and the synthesis of phytochemicals. The project will also optimize a process to produce such added-value compounds from undifferentiated Cannabis cells. This procedure allows the production of phytochemicals without the need to grow plants, by using cell suspension cultures. Such cultures grow under controlled and aseptic conditions in bioreactors of different volumes.

Abstract

Probability theory is the branch of mathematics dealing with the rigorous study of random phenomena. The aim of this project is to study new ways of quantifying and controlling the random fluctuations of large random systems, emerging in several domains, such as Statistics, Mathematical Physics and Stochastic Geometry. One of the themes common to the many venues explored in the project is that of applying variational techniques, involving several stochastic (and possibly, infinite-dimensional) versions of derivative and difference operators, as well as integration by parts formulae, from classical analysis.