This lecture by Alex Fink from Queen Mary University explores Speyer's tropical f-vector conjecture and its proof as part of the "Combinatorial Synergies in Geometry and Number Theory" workshop organized by the Instituto de Matemática Pura e Aplicada. Delve into the intersection of combinatorial methods with algebraic geometry and number theory in this 55-minute presentation that contributes to the broader workshop goal of enhancing combinatorial approaches to geometric and arithmetic structures. The workshop features mini-courses and presentations by international mathematicians focusing on topics like Hodge Theory, Berkovich Spaces, Tropical Geometry, matroids, and polynomial equations, bringing together both established specialists and early-career mathematicians to foster collaboration in these interconnected mathematical fields.