Evgeny Shinder  

Title: Factorization centers, Cremona groups and the Grothendieck ring of varieties

Abstract: I will state the question of uniqueness for centers of blow ups and blow downs of birational maps, 
explain what is currently known and give two applications. The first is to the structure of Cremona groups, 
namely their nongeneration by involutions in dimension >= 3. The second application is for the Grothendieck 
ring of varieties, of dimension <= 2, over perfect fields. Based on joint work with H.-Y. Lin, and with H.-Y. Lin 
and S. Zimmermann.