ED Mathématiques et Informatique
Algorithmic applications of Hecke operators of finite groups to Galois representations
by Fabrice ETIENNE (IMB - Institut de Mathématiques de Bordeaux)
The defense will take place at 15h30 - Salle de conférences Institut de Mathématiques de Bordeaux Université de Bordeaux Bâtiment A33, premier étage 351, cours de la Libération 33405 TALENCE FRANCE
in front of the jury composed of
- Aurel PAGE - Chargé de recherche - Université de Bordeaux - Directeur de these
- Alex BARTEL - Full professor - Glasgow University - Rapporteur
- Claus FIEKER - Full professor - University of Kaiserslautern-Landau - Rapporteur
- Alice PELLET--MARY - Chargée de recherche - Université de Bordeaux - Examinateur
- Céline MAISTRET - Maîtresse de conférences - University of Bristol - Examinateur
- Christian MAIRE - Professeur des universités - Institut FEMTO-ST - Examinateur
Let G be a finite group, and let H,J be two subgroups of G. Let R be a commutative ring, and V a R[G]-module. To every element of the free R-module on the set of double classes R[H G /J], we can canonically associate a morphism of R-modules from V^J to V^H, the sets of fixed points under the actions of J and H respectively. The morphisms associated with the classes HgJ, with g in G, are called Hecke operators. In this thesis, we will study the properties of Hecke operators, and in particular in the case where R = Z, and where the module V is the group of invertible elements of a number field K, Galois over Q, of Galois group G. Then, the action of a Hecke operator associated with a class HgJ sends the group of invertible elements of K^J to that of K^H. We develop two algorithmic applications of these properties. First, we develop an algorithm to compute by induction the class group of a number field of the form K^H, by reducing the problem to the same computation for smaller degree fields, of the form K^Ji, on the condition that the groups G, H, and the Ji satisfy a certain type of relations that we will call "generalised norm relations". We will study the properties of these relations. Then, given a finite Galois module M, we will describe an algorithm to find a resolution of M, where the morphism come in the form of sums of Hecke operators. And with such a resolution, we will develop an algorithm to compute the Selmer groups of the module M.
ED Sciences et environnements
Viability of forest management under an uncertain environment: application to the Landes de Gascogne pine forest in the 21st century.
by Clémence LABARRE (ISPA - Interaction Sol-Plante-Atmosphère)
The defense will take place at 14h00 - Salle de conférence ISPA 71 Avenue Edouard Bourlaux, Bâtiment ISPA, Salle de conférence 33140, Villenave d'Ornon
in front of the jury composed of
- Denis LOUSTAU - Directeur de recherche - Université de Bordeaux - Directeur de these
- Marielle BRUNETTE - Directrice de recherche - INRAE - Rapporteur
- Margarida TOME - Full professor - Universidade de Lisboa Instituto Superior de Agronomia - Rapporteur
- Thomas KNOKE - Professeur - TUM School of Life Sciences - Examinateur
- Jean-Christophe PEREAU - Professeur - Université de Bordeaux - Examinateur
- Jean-Christophe DOMEC - Professeur - Bordeaux Sciences Agro - CoDirecteur de these
Forests provide essential ecological functions, including timber production, carbon storage, and biodiversity conservation. These services strongly depend on the structure and composition of forest stands, which are themselves shaped by climate and both natural and human-induced disturbances. In a context of global warming, intensifying droughts, and multifactorial crises, these dynamics are being profoundly disrupted, raising major uncertainties about the future resilience of forests. In response to these challenges, forest planning must optimize productivity, adaptability, and the preservation of ecosystem services. However, conventional optimization models remain limited in their ability to incorporate complex spatial and temporal scales. Viability theory offers an alternative by assessing the feasibility of management objectives in a changing environment. It defines critical thresholds between production and adaptive capacity, thus enriching classical methods. My thesis compares and explores these approaches through the case of the Landes de Gascogne forest, a region both heavily exploited and highly exposed to risks. This forest has been weakened by extreme events such as storms Martin and Klaus, as well as wildfires. Drawing on viability theory, I used various optimization approaches to identify management trajectories suited to the region over the 2000–2100 period. The scenarios were derived from a dynamic model simulating forest stand responses to climate. At the regional scale, I identified strategies that reduce stand vulnerability while maintaining production levels. Spatial optimization highlights the importance of explicitly modelling disturbances for effective planning. These results contribute to the development of management tools that integrate forest system complexity and local stakeholder constraints. Ultimately, my work emphasizes the trade-offs between service production and forest resilience, and shows that a diversified management strategy enhances forest adaptability to both climate and societal challenges. This methodology can be applied to other forest contexts to support sustainable forest management.