Introduction

This school aims 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 and 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, symmetric functions, and character theory, will also be addressed, along with advanced topics like the Kostant Weight Multiplicity Formula or topological methods related to simplicial complexes, and the combinatorics of Coxeter groups. Through a combination of lectures, problem-solving sessions, and collaborative research, the participants will deal in detail with current research areas and open problems in algebraic combinatorics and combinatorial commutative algebra.

Venue: Syed Babar Ali School of Science and Engineering, Lahore University of Management Science, DHA, Lahore-PAKISTAN