In this programmatic talk, we will sketch both a conceptual and formal framework for reasoning about the notion of algorithm. This framework will arise from the analysis we will make of the relationships existing between the notion of algorithm and other similar (but still different) notions, like that of computation and that of program. We will first show that the Turing-Church thesis concerning effective computability is not sufficient to capture the notion of algorithm, as it identifies programs which are intensionally different. We will then show the limits of the existing models of computation in capturing some basic construction processes that we are willing to call algorithmic. In order to solve this problem, we propose a formalisation of the notion of model of computation on the base of which we claim that the notion of algorithm could eventually be analyzed. This approach centered around the dynamics of program execution, reconciles the more mechanical view of computation (such as formalized by Turing machines and automata) with the logical view - as it in particular stems from a generalization of Jean-Yves Girard's Geometry of Interaction programme.[-]

A (pseudo)-Anosov flow on a 3-manifold can be understood through its orbit space, a bifoliated plane with a natural action of the fundamental group of the manifold. In this minicourse, we will describe techniques to study the dynamics of these orbit space actions as a means to understand the topological theory and the classification of (pseudo)Anosov flows in dimension 3. This leads to a more general theory of 'Anosov-like' actions on bifoliated planes, which form a rich class of discrete dynamical systems including but not limited to the orbit space actions from flows.[-]

A (pseudo)-Anosov flow on a 3-manifold can be understood through its orbit space, a bifoliated plane with a natural action of the fundamental group of the manifold. In this minicourse, we will describe techniques to study the dynamics of these orbit space actions as a means to understand the topological theory and the classification of (pseudo)Anosov flows in dimension 3. This leads to a more general theory of 'Anosov-like' actions on bifoliated planes, which form a rich class of discrete dynamical systems including but not limited to the orbit space actions from flows.[-]

A (pseudo)-Anosov flow on a 3-manifold can be understood through its orbit space, a bifoliated plane with a natural action of the fundamental group of the manifold. In this minicourse, we will describe techniques to study the dynamics of these orbit space actions as a means to understand the topological theory and the classification of (pseudo)Anosov flows in dimension 3. This leads to a more general theory of 'Anosov-like' actions on bifoliated planes, which form a rich class of discrete dynamical systems including but not limited to the orbit space actions from flows.[-]