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 2connected curves a Cliffordtype 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 3connected curves. This is a joint work with M. Franciosi.

Mon 14 Jan 2013 16:00 
Santorio, room 136 
Kurusch Ebrahimi Fard
()

Exponential renormalization

Abstract.

Thu 10 Jan 2013 16:30 
Santorio, room 136 
Prof. Giovanni Marelli
(Universidad de Antioquia, Medellin, Colombia)

Gradientlike 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 gradientlike 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 $m(p)+ns$, 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 MorseWitten 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 ddimensional 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=n2 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.
