Thursday, Dec 2nd, 11:10am-12noon (Room SC1310)

Speaker:  Clover May (NTNU)

Title: Structure theorem for RO(G)-graded equivariant cohomology

Abstract: For spaces with an action by a group G, one can compute an equivariant analogue of singular
cohomology called RO(G)-graded Bredon cohomology.  Computations in this setting are often challenging
and not well understood, even for G = C_2, the cyclic group of order 2.  In this talk, I will start with an
introduction to RO(G)-graded cohomology and describe a structure theorem for RO(C_2)-graded
cohomology with (the equivariant analogue of) Z/2-coefficients.  The structure theorem describes
the building blocks for the cohomology of C_2-spaces and makes computations significantly easier. 
It shows the cohomology of a finite C_2 space depends only on the cohomology of two types of
spheres, representation spheres and antipodal spheres.  I will give some applications and talk about work in
progress generalizing the structure theorem to other settings. (Contact Person: Anna Marie Bohmann)
            

   
            

                Wednesday, Dec 8th, 12:10pm-1:00pm (Room SC1312)

Speaker:  Mitchell Faulk (Vanderbilt University)   

Title: Embedding Deligne-Mumford stacks into GIT quotient stacks of linear representations

Abstract: Ordinary Kodaira embedding uses an ample invertible sheaf to embed a proper variety into a projective space.
We obtain an extension to stacks with finite stabilizer groups: we are able to use a suitably ample locally free sheaf
over a proper Deligne-Mumford stack to furnish an embedding of the stack into a geometric invariant theory (GIT)
quotient stack constructed from a finite-dimensional linear representation of the general linear group.

 
              
              
                
                Shanks Workshop: "Interactions in Complex Geometry", December 11-12, 2021, Vanderbilt University