Log and Tropical geometry: an application desingularization of low genus stable maps to projective space
In the first part of the talk I will recall a few basic notions of toric geometry and try to explain how log geometry generalises them. Afterwords, we will see how this framework is helpful to interpret blow ups in a modular fashion. Finally, we will see in the examples of maps to projective space of low genus how these techniques apply to give a modular resolution of the main component of Kontsevich's space of stable maps.
(30 minutes general talk followed by 45 minutes research talk)