Combinatorial Algebraic Geometry: Weierstrass points on algebraic curves and tropical curves

An algebraic curve of high genus can be a difficult landscape to navigate. In such a situation, we would like a set of well-placed landmarks as a guide. This is what Weierstrass points provide for us. We will cover the definition of Weierstrass points, and overview results that quantify in what sense they are "well-placed". We will also mention some applications in algebraic geometry and tropical geometry, in particular:

• When does an algebraic / tropical curve have finitely many automorphisms?
  

• When is the moduli space of algebraic / tropical curves "general type"?