2026

The main aim of this school is to introduce young researchers and graduate students to fundamental and advanced tools of homological algebra as applied to non-commutative algebra and number theory, with an emphasis on algebraic, geometric, topological, and numerical methods.

The CIMPA School in Pernambuco, scheduled for January 2026, will bring together young researchers and experts in applied mathematics to explore cutting-edge topics such as mathematical modeling in neuroscience, epidemiological systems, topological data analysis in complex systems, and statistical mechanics of neural networks.

This CIMPA school aims to introduce graduate students and early-career researchers to the diverse fields of combinatorics and graph theory. It will highlight their wide-reaching applications and connections to other areas of mathematics and beyond.

The CIMPA school offers a comprehensive and advanced curriculum focused on optimization, mathematical programming, and their applications across various fields. The courses delve into both theoretical foundations and practical methodologies, covering topics such as nonsmooth optimization, integer linear programming, linear optimization, separation theorems, dynamic optimization, and monotone operator theory.

El objetivo de la escuela es brindar a los estudiantes un panorama amplio de los tópicos centrales del análisis numérico de ecuaciones en derivadas parciales, transitando un amplio panorama que desarrolla temas clásicos y técnicas avanzadas de elementos finitos y sus aplicaciones. Se dictarán ocho cursos en total, cuatro durante la primera semana (Ciudad de Rosario) y cuatro en la segunda (Ciudad de Buenos Aires).

This research school offers an intensive program covering advanced topics in symplectic topology, differential geometry, and related topics. Through introductory courses, exercise sessions, and advanced lectures, participants will explore fundamental questions such as the symplectic non-squeezing theorem, rigidity of Lagrangian intersections, random nodal sets, and convex integration for solving nonlinear differential constraints. In addition to theoretical aspects, programming sessions will allow participants to apply modern computational methods to solve partial differential relations.

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).

Over the last half a century, Algebra, Combinatorics, and Discrete Geometry have undergone transformations due, in part, to the connections each of these areas have to other fields and the growth of computational approaches used in the study of theoretical mathematics. These areas are closely intertwined, with various algebraic, combinatorial, and geometric objects playing pivotal roles. This CIMPA school aims to highlight the interactions between these areas and emphasize that combinatorics is more than a tool, but a research area that creates bridges.

The aim of this school is to explore and deepen the multifaceted connections
between algebra and combinatorics, highlighting how these fields influence and
enhance each other. The curriculum covers foundational topics such as graded
rings, Hilbert functions, free resolutions, and the relationship between symbolic
powers of ideals as well as the geometric properties of varieties, with a particular
focus on monomial ideals and their connections to graphs and simplicial
complexes. Key aspects of representation theory, including Young tableaux,