Pre-Seminar: Coherent sheaves on \$P^n\$ after Beilinson
Tue, May 2, 1:30pm – 2:30pm
In his demurely-titled 1.5 page paper "Coherent sheaves on \$P^n\$ and problems of linear algebra", Beilinson gave an explicit description of the derived category of coherent sheaves on the projective space. I will give an exposition of Beilinson's result together with some related recent advances.
Seminar: A power structure over the Grothendieck ring of pretriangulated categories
Tue, May 2, 2:30pm – 3:30pm
The notion of a power structure is closely related to that of a lambda ring. It is a powerful way to encode operations on certain generating functions. Gusein-Zade, Luengo, and Melle-Hernandez have defined a power structure over the Grothendieck ring of varieties. I will discuss an analog of this on a version of the Grothendieck ring of pretriangulated categories, whose elements represent enhancements of derived categories of coherent sheaves on varieties.