2021

Mathematical Logic is a subfield of mathematics exploring the applications of formal logic to mathematics. Its inception was motivated by the study of foundations of mathematics and it has found applications in many areas, specially in Theoretical Computer Science. The four pillars of Mathematical Logic are Set Theory, Recursion Theory, Model Theory and Proof Theory. This school intends to cover all such subjects, on different levels and with different applications.  The proposed tree basic courses have the great advantage of requiring no or little prior knowledge.

The courses are introductory to carry research activity in contemporary trends in Hodge Theory and p-adic Hodge Theory given by main actors in each activity: Hodge structures, Hodge-Tate structures, De Rham Cohomology and Betti Cohomology, Torelli type theorems, Abelian Varieties.

This  school  aims  to  introduce  young  researchers  and  students  to  actual research  problems  in  the  field  of  tilings,  packings  and  optimization.  In particular,  we  shall  focus  on  possible  original  interactions between  these thematics, as well  as connections with more classic fields as number theory, transportation modeling or word combinatorics.

The main theme of the proposed school are graph algebras, which are objects of growing interest that lie at the boundary between algebra and analysis among other mathematical fields. Despite being introduced only about a decade ago, Leavitt path algebras, as algebraic counterpart of graph C ∗ -algebras, have arisen in a variety of different contexts as diverse as symbolic dynamics, noncommutative geometry, representation theory, and number theory.

The school will provide an introduction to both basic and more advanced topics in the moderntheory of dynamical system and ergodic theory. It will be aimed mostly at Masters level students and thus assume a reasonable general mathematical background but no previous specialised knowledge in the topics covered in the courses. The scientific content of the various courses will be tightly coordinated in order to provide the students with the possibility of a real concrete learning experience which can become the foundation for further study.

The summer school will be dedicated to finite point configurations and rigidity, Erdos problems in discrete geometry and frame theory, the Falconer distance conjecture  in  geometric  measure  theory,  discrete  integrable  systems  and connections between these topics.  Participants will  be introduced to various open problems and possible research projects  in these very active research areas.

Langue officielle de l'école : anglais

The goal of this CIMPA research school is twofold. First of all, the school offers a rigorous introduction to the theoretical bases of optimization and optimal control.