"Factorization theorems for volume preserving birational maps of Calabi–Yau pairs (following A. Corti and A.-S. Kaloghiros)

In 2010 J. Blanc proved that the group of symplectic birational automorphisms of $\mathbb{CP}^2$ is generated by $\mathrm{SL}_2(\mathbb{Z})$, $(\mathbb{C}^*)^2$, and a certain map of order $5$. In this talk I'll try to explain some results which generalise the theorem of Blanc in the same way that the Sarkisov program generalises M. Noether's theorem on the generators of the Cremona group of $\mathbb{CP}^2$.