Factorization Centers in Dimension Two and the Grothendieck Ring of Varieties

Explore a 56-minute lecture on factorization centers in dimension two and their connection to the Grothendieck ring of varieties. Delve into the concept of factorization centers for birational isomorphisms, focusing on smooth projective surfaces over perfect fields. Discover how these centers are independent of the choice of isomorphism and only depend on the surfaces involved. Examine the proof, which utilizes the two-dimensional Minimal Model Program and link decomposition for morphisms. Investigate the relationship between factorization centers and the rationality problem for surfaces, as well as their impact on the structure of the Grothendieck ring of varieties. Follow along as the speaker, Evgeny Shinder from the University of Sheffield, presents joint work with H.-Y. Lin and S. Zimmermann, covering topics such as minimal rational surfaces, rationality centers, Sarkisov links, and del Pezzo surfaces of degree 6.