Tropical linear series and applications to number theory and algebraic geometry

After formulating the Riemann-Roch theorem for graphs and tropical curves and the “Specialization Lemma relating them to the classical Riemann-Roch theorem, I will discuss reduced divisors, which are certain special and extremely useful representatives for linear equivalence classes. I will then describe recent applications of such theorems and tools to rational points on algebraic curves and Brill-Noether theory.