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International audience; In 1980, Janusz A. Brzozowski presented a selection of six open problems about regular languages and mentioned two other problems in the conclusion of his article. These problems have been the source of some of the greatest breakthroughs in automata theory over the past 35 years. This survey article summarizes the state of the art on these questions and the hopes for the next 35 years.; En 1980, Janusz A. Brzozowski a présenté une sélection de six problèmes ouverts sur les langues réguliers et mentionné également deux autres problèmes dans la conclusion de son article. Ces problèmes ont été à l'origine de quelques-unes des plus grandes percées dans la théorie des automates cours des dernières 35 années. Cet article de synthèse résume l'état de l'art sur ces questions et les espoirs pour les 35 prochaines années.

International audience; This article presents the analysis of ordinary practices of five primary school teachers when they teach open problems in class during mathematics sessions (Arsac & Mante 2007). The practices are ordinary because we intervened neither in the choice of the problems nor in the implementation of the sessions. The five teachers were observed during a school year, during the sessions which they dedicated to open problems. This research is organized within the framework of the didactic and ergonomic approach (Robert & Rogalski 2002) while using the notions of professional gestures and routines (Butlen 2004). By identifying the professional gestures and routines of the five teachers associated with devolution, regulation and institutionalization moments, we determine two teachers’ profiles associated to the study of open problems in class.; Este artículo presenta parte de una investigación realizada en el marco de una tesis doctoral. Da cuenta del análisis de las prácticas habituales de cinco profesores de primaria cuando proponen problemas abiertos en clase de matemáticas (Arsac & Mante 2007). Las prácticas son habituales por el hecho de que no intervinimos en la elección de los problemas ni en la preparación y ejecución de las sesiones. Los cinco profesores han sido observados a lo largo de un año escolar, durante las sesiones dedicadas a los problemas abiertos. El estudio se realizó en el cuadro del doble enfoque didáctico y ergonómico (Robert & Rogalski 2002) utilizando los conceptos de gestos y rutinas profesionales (Butlen 2004). Hemos identificado, para cada profesor, los gestos y rutinas profesionales asociados con los momentos de devolución, regulación e institucionalización, identificando dos perfiles de profesores asociados con el estudio de los problemas abiertos en clase.; Cet article présente une partie d’une recherche menée dans le cadre d’une thèse. Il rend compte de l’analyse des pratiques ordinaires de cinq professeurs des écoles lorsqu’ils proposent en classe, pendant les cours de mathématiques, des problèmes ouverts (Arsac & Mante 2007). Les pratiques sont ordinaires au sens où nous ne sommes intervenus ni dans le choix des problèmes, ni dans la mise en œuvre des séances. Les professeurs ont été observés tout au long d’une année scolaire, lors des séances qu’ils dédient aux problèmes ouverts. L’étude a été menée dans le cadre de la double approche didactique et ergonomique (Robert & Rogalski 2002) tout en utilisant les notions de gestes et de routines professionnels (Butlen 2004). En repérant, pour chaque professeur, les gestes et routines professionnels associés aux moments de dévolution, de régulation et d’institutionnalisation, nous identifions deux profils d’enseignants associés à l’étude de ces problèmes en classe.

Analytic number theory deals with the application of analysis, both real and complex, to the study of numbers. It includes primes, transcendental numbers, diophantine equations and other questions. The study of the Riemann zeta-function $\zeta(s)$ is intimately connected with that of primes. \par In this note, edited specially for this volume by K. Srinivas, some problems from a handwritten manuscript of Ramachandra are listed.

Proof and proving have been objects of investigation from the point of view of mathematics and mathematics education for the past few years. Historical and epistemological studies show that proof is a crucial activity within mathematical practice. Didactical studies show that students encounter many difficulties when approaching proving in the classroom. Research at a cognitive level has developed frameworks interpreting students' difficulties. Studies concerned with the use of new technologies have been investigating the use of tools to support students with proving. In particular, a strand of research has studied specifically the impact of dynamic geometry software with respect to the teaching and learning of proving in geometry. The main difficulty with respect to proof and proving that emerges from current research is the gap between empirical and theoretical elements involved with these activities. This study addressed the problem of how a dynamic geometry software (Cabri) may support students in managing the relationship between the spatio-graphical (empirical) field and the theoretical field. Through a detailed analysis of students' processes when working with open geometry problems involving conjecturing and proving in Cabri, an analytical and explanatory framework has been developed. This framework also takes into account interactions between the students and the tools used and between the students themselves. The research findings suggest that proving within a dynamic geometry environment develops as a focusing process, in which the shifts between ascending and descending processes between the spatio-graphical and the theoretical field appear to be key elements for the construction of conjectures and proofs. The analysis also shows that Cabri works as a shared workspace, i.e. as a space which supports the interaction between students' internal contexts and the construction of shared knowledge.

International audience; In this paper, some recent progress on stability, robust stability and control techniques on time-delay systems are outlined. The goal is to give an overview of the techniques encountered in the analysis and design of delay systems. The key point is the analysis of the effects of delays on the (closed-loop) system properties. Some open problems will be also discussed. This survey paper complements the guided tours presented in [42, 30, 45]. A different control perspective can be found in [53].