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Combinatorics is at the center of many areas in pure and applied mathematics. This summer school will focus on the versatility of combinatorics to shed light on problems in algebra, geometry, optimization, and mathematical physics. We will also discuss how algebraic and geometric perspectives can help us understand purely combinatorial objects. The main goal of the school is to bring young mathematicians from Colombia and other Latin American countries into close contact with each other and with world experts in various fields of combinatorics. This is part of a long term goal to build a strong regional community of mathematicians in combinatorics and related fields.