The representation theory of finite groups has been a very active area of mathematics for the past century. One reason for this is its numerous applications, not only within mathematics, but also in chemistry and physics. In several infinite families of groups, it turns out that there is a very strong link between the representation theory of these groups and the combinatorics involving certain objects (like integer partitions, crystal graphs or cell decompositions). In order to get important information about the irreducible representations, general representation theoretic methods are intertwined with the study of combinatorial properties of the objects labelling them. The aim of this project is to make progress on important conjectures in modular representation theory pertaining to the symmetric and other groups. To do this I propose to combine the tools developed by B. Külshammer, J. B. Olsson and G. R. Robinson on generalized blocks, in particular for symmetric groups, and my own research, especially recent results on defect groups and defects for characters and on basic sets.

Hyperthermia therapy is a medical treatment in which body tissue is exposed to high temperatures to damage and kill cancer cells or to make cancer cells more sensitive to the effects of radiation and certain anti-cancer drugs. Indeed, heating a living tissue at a temperature between 42°C to 46°C causes cell inactivation. The spectacular development of nanotechnology makes possible the use of heat sources at the nanoscale, activated by an external field. These nanosources provide decisive advantages compared to macroscopic implants. Among the different nanostructures proposed to mediate thermal ablation of cancerous cells, the use of magnetic nanoparticles is a very promising route. Indeed, the temperature increase required for hyperthermia can be achieved by using magnetic nanoparticles, which can be heated by the action of an external alternating magnetic field, because of the loss process that occurs during the reorientation of their magnetization. This project is focused on the development and the optimization of iron oxide nanostructures dedicated for magnetic hyperthermia. The goal of this proposal is to work on two relevant questions regarding the use of nanometric heat generators for therapeutic hyperthermia: (i) How can we maximize the heating capacity of the nanosources ? Magnetic hyperthermia depends on the size, shape, composition, atomic structure and local environment of the nanoparticles. It is therefore essential to understand the fine relation between these parameters and the heating properties of the nanosources. The atomic-scale characterization of the nanoparticles performed by using the outstanding performances of aberration–corrected electron microscopy, combined with magnetic measurements, will provide concrete explanations of the nanosource heating performances. These indispensable information will give us an unprecedented opportunity to synthesize optimized nanosources by using the flexibility of the present chemical fabrication methods. (ii) The therapeutic use of nanomaterials raises also the questions of the biodistribution and biodegradation of the nano-agents inserted into the patient body. Therefore, we will study the long-term aging of the nanosources in the cellular medium. We will use magnetic measurements adapted to characterization of nanoparticles in biological environment (ferromagnetic resonance, SQUID) and the multi-functionalities of transmission electron microscopy to highlight the structural and magnetic transformations due to the nanoparticles / cells interactions. This approach will give precious information on the nanosources toxicity, which are of high interest for a very broad scientist audience, since iron oxide nanoparticles have numerous biomedical applications (magnetic resonance imaging, guided drug and gene delivery, tissue engineering, cell tracking, bioseparation…).