Introduction

This school aims to explore and deepen the multifaceted connections between algebra and combinatorics, highlighting how ideas and techniques from these fields interact and enrich one another. The curriculum brings together foundational and contemporary topics in algebraic combinatorics, commutative algebra, algebraic geometry, and topology. It will cover algebraic and combinatorial structures such as monomial and binomial ideals, extremal ideals, ideals of 2-minors, graph ideals, Gröbner bases, toric and lattice ideals, as well as their connections with graphs, simplicial complexes, and matroids. The school will also introduce fundamental topics in algebraic combinatorics, including generating functions, partitions, Young tableaux, symmetric functions, partially ordered sets, Möbius inversion, graph polynomials, and matroid invariants. Further themes will include the combinatorics and topology of hyperplane and hypersurface arrangements, algebraic aspects of matroids, toric and tropical geometry, and topological methods such as homology, homotopy, shellability, and discrete Morse theory. Through a combination of lectures, problem-solving sessions, examples, and collaborative research activities, participants will engage with current research directions and open problems, while developing a broader understanding of how algebraic, combinatorial, geometric, and topological methods come together in modern mathematical research. 

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