The CEMRACS is a scientific event of the SMAI (the French Society of Applied and Industrial Mathematics). The concept was initiated in 1996 by Yvon Maday and Fr´ed´eric Coquel and takes place every year at CIRM in Luminy (Marseille, France) during 6 weeks from mid-July. The goal of this event is to bring together scientists from both the academic and industrial communities to work and discuss on focused topics. During the first week, a classical school is proposed. It consists of several lectures given by leading scientists and related to the topics of the research projects.

The thematic month Logic and Interations 2022 is an event proposed by the Logique de la Programmation group of the I2M, in relation with the LIS, the PPS group at IRIF, the logic group of Roma Tre university to enumerate the main partners. The goal is to establish the state of the art, train young researchers, open new research collaborations and trails in the domain of interactions between logic, philosophy and theoretical computer science, and more precisely between proof theory and formal methods.

This residential month is along the lines of former sessions organized at CIRM each February since 2001 by a group of Marseille researchers. In February 2020, the members of the Institute of Mathematics of Marseille involved in collaborations with biologists propose to gather researchers from around the world, at CIRM, around the theme of Mathematical Biology. The interplay between mathematics and biology has developed rapidly since the last decades of the 20th century, both in France and in all developed countries.

The theoretical study of quantum many-body systems is a challenging task due to the amazing complexity induced by the huge number of degrees of freedom of these systems. Equilibrium properties of such systems have been deeply studied in the last decades. In particular, at one-dimension, it is possible for some systems to have access to exact solutions, for instance, within Bethe Ansatz methods. Where exact solutions are not accessible, it is possible to use field theoretical approaches or numerical techniques.

Higher structures, in particular homotopy algebras, have appeared in many branches of mathematics and particularly in mathematical physics ranging from deformation theory, derived geometry, enumerative geometry, representation theory, homotopy algebras, Poisson geometry and quantization, mirror symmetry, noncommutative algebraic geometry, string theory and quantum field theory. This IHP trimester aims to promote interaction between mathematicians, physicists and groups working on related areas from different aspects.