Mexico

The school aims to introduce graduate students and young researchers to the recent connections between p-adic analysis (understood in a large sense) with mathematical physics and computer science. The courses will be focused on active research areas. The tentative list of courses include: (1) introduction to p-adic analysis; (2) introduction to local zeta functions; (3) p-adic models in quantum physics; (4) the p-adic theory of automata; (5) p-adic electrostatics; (6)  Strings amplitudes, local zeta functions, and log-Coulomb gases.

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.

The aim of the school is to introduce graduate students to the modern categorical methods in representation theory. The three courses of the first week will focus on the basic elements required for further topics. Thus, these courses will consist on brief recollections and introductions to: Categories and modules, group actions and bisets, linear representations of finite groups and block theory. For all of them there will be training sessions in the afternoons, where problems, doubts and related questions will be discussed.

The school aims to introduce graduate students and young researchers to the recent connections between p-adic analysis (understood in a large sense) with mathematical physics and computer science. The courses will be focused on active research areas. The tentative list of courses include: (1) introduction to p-adic analysis; (2) introduction to local zeta functions; (3) p-adic models in quantum physics; (4) the p-adic theory of automata; (5) p-adic electrostatics; (6)  Strings amplitudes, local zeta functions, and log-Coulomb gases.

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.

Differential equations are typically considered to be a subject of mathematical analysis or, more generally, "continuous mathematics". However, algebraic and discrete methods have been successfully applied to questions about differential equations such as, for example, finding symmetries or closed-form solutions. Recent years have witnessed significant development of constructive aspects of algebraic geometry and tropical algebra including deep theory and efficient algorithms.

The school aims to introduce graduate students and young re- searchers to the new trends in Hamiltonian systems and celestial mechanics. To this end, the school is articulated in five highly topical themes in the area, all sharing to a greater or lesser extent the classical N–body problem as a prototypical and paradigmatic case.

Langue officielle de l'école : anglais

This school aims at introducing interested mathematicians to the theory and practice of interactive theorem provers, such as Lean or Rocq (previously named Coq) and to spur collaboration between such mathematicians and current proof assistant expert users. This school targets participants with diverse backgrounds in mathematics, but without a specific knowledge in logic or program verification.

A number of significant breakthroughs have occurred in Commutative Algebra in the past couple of years. One revolution in the field is the application of perfectoid spaces to Commutative Algebra which has resolved a number of major open questions about rings of mixed characteristic, e.g., the direct summand conjecture (as solved by André) and uniform comparison of symbolic powers and ordinary powers in regular rings (established by Ma and Schwede).