Explore a lecture on solving equations from combinatorics using computer algebra techniques. Delve into the world of enumerative combinatorics and its complex problems, focusing on Discrete Differential Equations. Learn about the enumeration of walks, planar maps with hard particles, and other related challenges. Discover how these functional equations connect formal power series in multiple variables to their specializations. Examine Popescu's 1986 result on algebraicity of solutions for nested variables, and understand the elementary proof provided by Bousquet-Melou and Jehanne in 2006 for the two-variable case. Investigate a recent approach that utilizes effective algebraic geometry to solve equations more efficiently in the two-variable scenario. Explore recent advancements in solving systems of such equations. This talk, presented by Hadrien Notarantonio from INRIA Saclay, is based on collaborative work with Alin Bostan, Mohab Safey El Din, and Sergey Yurkevich.