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.

Intro
Motivation: main question
Main result for this talk: dim(X) = 2
Axiomatic definition for có
Examples
Grothendieck ring and Open questions
2-truncated Grothendieck group
A diagram
Surface? What surface?
Minimal rational surfaces are models of large degree
Rationality centers
Reformulation of the main result for rational surfaces
Sarkisov links
Proof of the main theorem for rational surfaces
Link of the day: del Pezzo surfaces of degree 6
Summary