University of Utah


Click on the title of a talk for the abstract (if available).
Date  Speaker  Title  
February 3  Emanuele Macrì 
A categorical invariant for cubic threefolds


February 10 

Exceptional loci on moduli spaces of rational npointed curves
The GrothendieckKnudsen moduli space of stable, npointed rational curves
is a fascinating variety whose geometry is still little understood. In
particular, one would like to understand its effective cones (of curves or
of divisors), its birational modifications, etc. A natural question is if
boundary strata generate these cones. This is false for divisors by an
example of Keel and Vermeire (for n=6) and still unknown for curves (this
is known as the Fulton Conjecture). In some joint work with Jenia Tevelev,
we identify the interior of the moduli space with a BrillNoether locus of
various very special reducible curves associated to hypergraphs. This
allows us to construct factorially many new extremal (nonboundary)
divisors of the effective cone, as well as some rigid curves and morphisms
with small exceptional locus.


February 17 

Stable pairs on elliptic K3 surfaces
We consider a smooth K3 elliptic surface S with a section and we investigate the behaviour of moduli spaces of pairs on it. For a suitable choice of the framing, we get a finite family of moduli spaces related by wall crossing phenomena giving rise to birational maps. In a particular case, this allows to recover an isomorphism (described by Friedman with different techniques) between a moduli space of rank two coherent sheaves on S and the Hilbert scheme.



The seminar is canceled




Deformations of K3 surfaces and orientation
We present a generalization of the Derived Torelli Theorem to first order deformations of the derived categories of K3 surfaces. This result shows that the equivalences between such categories is detected by the existence of special isometries of a first order deformation of the Mukai lattice. A key ingredient in the proof is the fact the such isometries preserve the orientation of a 4dimensional subspace in the cohomology of the surfaces. This is joint work with E. Macrì and, partially, with D. Huybrechts.


March 24  Jimmy Dillies 
On dessins d'enfants I


March 31  Aaron Bertram 
Bridgeland stability and quasistability for surfaces, and some wild speculation in higher dimensions


April 7  Enka Lakuriqi 
Introduction to Mirror Symmetry


April 28  Remi Lodh 
On a generic hyperplane section of certain singular schemes over a field
I will explain why a generic hyperplane section of a logsmooth
scheme over a type of logpoint is again logsmooth. A special case is
that of toric singularities. We will make use of the language of
logarithmic structures (in the sense of FontaineIllusieKato) and so we
will give a brief introduction to this language.

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