Past seminars 2013 (go back to current seminars)

When Where Who Title (Click for abstract)
Wed 16 Jan 2013 16:30 Santorio, room 136 Elisa Tenni (SISSA) Clifford theorem for singular curves and some applications
Abstract. Abstract: I will discuss a generalization of the classical Clifford's theorem to singular curves, reducible or non reduced.
I will prove that for 2-connected curves a Clifford-type inequality holds for a vast set of torsion free rank one sheaves. I intend to show that our assumptions on the sheaves are the most natural when working with this kind of results.
I will moreover show that this result has many applications to the study of the canonical morphism of a singular curve, in particular that it implies a generalization of the classical Noether's theorem to 3-connected curves.
This is a joint work with M. Franciosi.

Mon 14 Jan 2013 16:00 Santorio, room 136 Kurusch Ebrahimi Fard () Exponential renormalization
Thu 10 Jan 2013 16:30 Santorio, room 136 Prof. Giovanni Marelli (Universidad de Antioquia, Medellin, Colombia) Gradient-like vector fields on a complex analytic variety
Abstract. Given a complex analytic function $f$ on a Whitney stratified complex analytic variety of complex dimension $n$, whose real part $Re(f)$ is Morse, we prove the existence of a stratified gradient-like vector field for $Re(f)$ such that the unstable set of a critical point $p$ on a stratum $S$ of complex dimension $s$ has real dimension $m(p)+n-s$, where $m(p)$ is the Morse index of the restriction of $f$ to $S$, as was conjectured by Goresky and MacPherson. We expect as application the construction of the Morse-Witten complex for intersection homology.
Wed 9 Jan 2013 16:30 Santorio, room 136 Dr. Ada Boralevi (SISSA) Spaces of matrices of constant rank and instantons
Abstract. Abstract: Given a complex vector space V of dimension n, one can look
at d-dimensional linear subspaces A in \Wedge^2(V), whose elements
have constant rank r. The natural interpretation of A as a vector
bundle map yields some restrictions on the values that r,n and d can
attain. After a brief overview of the subject and of the main
techniques used, I will concentrate on the case r=n-2 and d=4. I will
introduce what used to be the only known example, by Westwick, and
give an explanation of this example in terms of instanton bundles and
the derived category of P^3. I will then present a new method that
allows to prove the existence of new examples of such spaces, and show
how this method applies to instanton bundles of charge 2 and 4. These
results are in collaboration with D.Faenzi and E.Mezzetti.