There is a pleasing correspondence between splittings of a free group over finitely generated subgroups and systems of surfaces in a doubled handlebody. One can use this to describe a family of hyperbolic complexes on which Out(F_n) acts. This is joint work with Camille Horbez.
The moduli space of cubic surfaces is known to be isomorphic to a quotient of the unit ball in C^4 by an arithmetic
group. We review this construction, then explain how to construct
an explicit inverse to the period map by using suitable theta functions. This gives a new proof of the isomorphism between the two spaces.
The effective cone of the Hilbert scheme of points in $P^2$ has
finitely many chambers corresponding to finitely many birational models.
In this talk, I will identify these models with moduli of
Bridgeland-stable two-term complexes in the derived category of
coherent sheaves on $P^2$ and describe a
map from (a slice of) the stability manifold of $P^2$
to the effective cone of the Hilbert scheme that would explain the
correspondence. This is joint work with Daniele Arcara and Izzet Coskun.
We report on joint work with Arend Bayer on the space of stability conditions for the canonical bundle on the projective plane.
We will describe a connected component of this space, generalizing and completing a previous construction of Bridgeland.
In particular, we will see how this space is related to classical results of Drezet-Le Potier on stable vector bundles on the projective plane. Using this, we can determine the group of autoequivalences of the derived category. As a consequence, we can identify a $\Gamma_1(3)$-action on the space of stability conditions, which will give a global picture of mirror symmetry for this example.
In the second hour we will give some details on the proof of the main theorem.
We report on joint work with Arend Bayer on the space of stability conditions for the canonical bundle on the projective plane.
We will describe a connected component of this space, generalizing and completing a previous construction of Bridgeland.
In particular, we will see how this space is related to classical results of Drezet-Le Potier on stable vector bundles on the projective plane. Using this, we can determine the group of autoequivalences of the derived category. As a consequence, we can identify a $\Gamma_1(3)$-action on the space of stability conditions, which will give a global picture of mirror symmetry for this example.
In the second hour we will give some details on the proof of the main theorem.