2026

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,

The CIMPA school on Algebraic Geometric Methods in Information Theory will focus on the applications of algebraic geometry and number theory to coding theory and cryptography, providing a thorough introduction to both the theoretical foundations and practical applications of these mathematical tools in information theory.

This summer school aims to promote collaboration between Nepalese and international researchers, with a focus on early-career scholars. It provides research scholars from Nepal and neighboring countries an opportunity to strengthen their modeling, computational, and analytical skills, essential for addressing nonlinear phenomena in fields such as socioeconomics, environmental science, biology, public health, and natural sciences.