Luxembourg National Research Fund

The FNR is pleased to communicate the results of the 2022 OPEN Call for proposals: 3 of 6 eligible projects have been retained for funding, an FNR commitment of 1.5 MEUR. 1 additional project is on the reserve list.

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.

Go to OPEN programme page

Funded projects

Abstract

A moduli space is a record-keeping device used by an algebraic geometer: every point in this “”shape”” corresponds to a specific object in a class of objects that you are trying to classify. It is a dictionary, except that the words are allowed to blur over into each other. It is itself a shape that records a collection of other objects, and how they are related to each other.

An algebraic geometer often starts by studying 1-dimensional shapes, or curves: they are the simplest interesting objects. One important tool in the study of curves is the classification of vector bundles on them: it’s like understanding a natural habitat by knowing which plants and animals live in it. And whilst a biologist will classify the plants and animals in the habitat into a list and relations between the different species, an algebraic geometer will construct a new geometric shape: the moduli space parameterizing vector bundles on the curve.

The goal of the project is to transport what we know for vector bundles on curves to other contexts: quivers and their representations, and Brauer-Severi schemes of hereditary orders. These are also 1-dimensional in the appropriate sense. The biggest difference is that they are of noncommutative origin, yet we can still associate moduli spaces to them. By understanding what remains true when going from commutative to noncommutative, we gain a deeper understanding in why things are true in the original context, and what is universal amongst all settings.

Abstract

In 2009, the PI and G. Peccati introduced a method, typically referred to as Malliavin-Stein (M-S) approach, which combined for the first time Stein’s method with infinite-dimensional integration by parts formulae based on the use of Malliavin-type operators. Since then, this theory has never ceased to grow and has reached today the status of an essential tool of modern stochastic calculus, with regular additions and diverse applications well beyond the context in which it was initially introduced (Gaussian space). Since several years, the mathematics department of the University of Luxembourg has been a major player in the development of the M-S approach. One of our ambition with FraMStA is to further establish our position of global leaders in this domain.

The rapid development of the M-S approach was facilitated by the fact that it applied particularly well to the derivation of limit theorems for nonlinear functionals of the fractional Brownian motion (fBm). The study of this process, which is a genuine extension of the standard Brownian motion, poses many challenges, related in particular to the fact that fBm is neither Markovian nor a semimartingale. Nowadays, fBm plays a major driving role in the development of the M-S approach, similar to the crucial place it occupies in the theory of rough paths, which is in turn tightly connected to Martin Hairer’s Fields Medal (2014).

The main goal of FraMStA is to further advance the development of the M-S approach and the analysis of fBm in non-standard situations, using tools from stochastic analysis, convex geometry, differential geometry and stochastic analysis. To achieve it, we will rely on two junior researchers who will work on the themes of the project. We will also invite world renowned specialists and organize a workshop and a conference.

Abstract

Public concerns about the environment and the detrimental impact of pesticides make that fewer and fewer tools to ensure production are available for farmers. Nonetheless, studies show that banning the use of fungicides results in a decreased agricultural production, thereby further endangering the need to feed a growing world population. For these reasons, there is a huge effort ongoing to find new, environmental-friendly fungicides and these are searched in bacteria, fungi and plants.

Plants cannot run away from unfavourable conditions, but they have, through evolution, developed a number of mechanisms that allow them to survive non-optimal conditions, including exposure to pathogens. One of these mechanisms is the synthesis and accumulation of small molecules with activities that protect plants from infections. Among these compounds, saponins are known and studied to protect plants from fungal infections. However not all plants produce the same saponins and this in different quantities, furthermore not all fungi have the same sensitivity for saponins.

Mining data from previous projects resulted in the identification of saponins in stems from different Fabaceae, and it was seen that the conditions wherein these plants grow have an impact on the composition of the saponin pools of these plants. Based on this TASSILI will provide the fundamental data for further studies towards the production of saponin-based fungicides extracted from locally-grown Fabaceae (alfalfa, peas, soybean and faba bean).

Extracts will be made from different varieties of the mentioned plants. This will generate a set of extracts with different composition and thus potentially different fungicidal activities against plant pathogenic fungi. The activity of these extracts will be tested against some common plant pathogenic fungi: Botrytis cinerea (a pathogen in viticulture), Fusarium graminearum and Zymoseptoria tritici two important pathogens in grain cultivation. By testing a diverse set of extracts against these fungi, TASSILI will result in the correlation between the composition of the extracts and the measured fungicidal activity. Furthermore, the saponins that contribute most to this activity will be identified.