Abstract: REGS Day presentations: Pizza party and awarding of prizes follows.
Matthew Mastroeni, Matrix Factorizations and Singularity Categories in Codimension Two
A theorem of Orlov from 2004 states that the homotopy category of matrix factorizations on an affine hypersurface $Y$ is equivalent to a quotient of the bounded derived category of coherent sheaves on $Y$ called the singularity category. This past June, Eisenbud and Peeva introduced the notion of matrix factorizations in arbitrary codimension. As a first step towards generalizing Orlov's theorem to higher codimension, I will describe how to construct a functor from codimension two matrix factorizations to the singularity category of the corresponding complete intersection.
Meghan Galiardi, Evolutionary Dynamics in Finite Populations
Game theory is used to construct a Markov chain for a game between two populations of finite size. By looking at the large number limit, the Markov chain is approximated by a 1-parameter family of deterministic differential equations. All possible bifurcation diagrams for these differential equations are categorized and this result is compared with the initial Markov chain.
Daniel Hockensmith, Folded Symplectic Geometry
Toric symplectic manifolds may be classified using the topology of their quotient spaces and their moment map data. These constructions generally require the non-degeneracy of the symplectic form. We will discuss how one may circumvent this limitation in the case where the symplectic form is allowed to have fold singularities.