"Receptor proteins on the surfaces of B- and T-cells interact with pathogens, recognize them and initiate an immune response. The diversity and complexity of immune receptors poses a challenge to nonequilibrium many-body physics and our understanding of the physical principles that control the emergent functional properties of biological systems, such as recognition. The diversity of the composition of the immune repertoire emerges as a self-organized process, stimulated by interactions with the environment. The goal of the proposed research is to study the self-organization of the immune repertoire in the face of its pathogenic environment at the molecular and evolutionary level, by using a combination of data analysis and statistical mechanics modeling.Recent experiments have determined the set of B-cell receptors found in a zebrafish and T-cells in humans – data that allows for theoretical analysis and hypotheses rejection that were never possible before. I will theoretically study the problem of recognition from four unique and complementary directions:- guided by statistical signatures in the data I will propose evolutionary models of how selection and mutation in the sequences lead from the genomic precursors to a functional repertoire of receptors,- I will quantify, under simplifying assumptions, the question of the optimal repertoire for recognition in a varying but partially predictable pathogenic environment using maximum likelihood,- analyzing sequence data I will build probabilistic models to characterize the molecular scenarios that generate the repertoire,- I will use information theory and statistical methods to build data-driven models of the molecular nature of recognition based on yeast display experiments.Describing interactions between elements of receptor sequences will be an important step towards a physical understanding of recognition in the immune system, a crucial concept in grasping the onset of allergies and auto-immune diseases."