Some features about the geometry of certain moduli spaces (e.g, topological invariants)
suffer naturally a combinatorial explosion as the parameters used to build the moduli (like
the rank or genus of a curve) increase, making their analysis difficult. In this talk we will
explore some ways in which computers can help algebraic geometers tackle this situation.
Concretely, we will focus on two applications to moduli spaces of bundles on curves.

On the one hand, we will see how we can use binary classification trees to count the
number of possible non-isomorphic moduli spaces of parabolic vector bundles on a marked
curve and obtain their automorphism groups.

On the other hand, a new Python package will be presented which allows an efficient
computation and simplification of motivic expressions in the Grothendieck ring of varieties,
and we will see that the package can be used to verify computationally Mozgovoy’s
conjecture on motive of the moduli space of twisted Higgs bundles.

Joint works with Sergio Herreros, Javier Rodrigo, Daniel Sánchez, Jaime Pizarroso and José
Portela.