Using computational tools to study the geometry of moduli spaces

Seminario del IUFFyM

Using computational tools to study the geometry of moduli spaces

que impartirá el profesor

David Sánchez Alfaya

Universidad Pontificia de Comillas, Madrid

este jueves 20 (mañana) a las 13:00h en la sala de seminarios del IUFFyM, Facultad de Ciencias, Universidad de Salamanca.

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.