Algebra Seminar: Kelly -- Kuznetsov Categories for Gauged Linear Sigma Models

Tyler Kelly (Queen Mary University of London) will be speaking in the algebra seminar.
We will go out for lunch after the talk---all are welcome to join! 

When: 12-1pm Friday February 27 

Where: Carslaw 175 

Title: Kuznetsov Categories for Gauged Linear Sigma Models 

Abstract: The derived category of coherent sheaves on a variety X is a robust algebraic
invariant of a variety, holding a wealth of information.  For certain Fano varieties,
the derived category has very interesting admissible subcategories that hold the
majority of the geometric information.  For example, Kuznetsov identified a component of
the derived category of the cubic fourfold that looks much like the derived category of
a K3 surface, and used this information to identify interesting geometry about the cubic
fourfold.  This subcategory and some other examples of the same phenomenon are now
called Kuznetsov components of the derived category.  Unfortunately, the Kuznetsov
component has not been given a uniform definition.  In this talk, we propose a
definition of a Kuznetsov category for a gauged linear sigma model, an equivariant
curved variant of the derived category.  This definition allows us to create new study
of it.  We then provide some results that help justify our definition.  This is joint
work with David Favero and Dan Kaplan.