F. BASTIANELLI :

Title : Effective cycles on symmetric products of curves

Abstract : I will be concerned with the convex-geometric proerties of the cone of n-dimensional pseudoeffective

cycles in the d-fold symmetric product $C_d$ of a smooth curve $C$. In particular, I will show

that the cone generated by n_dimensional diagonal cycles is a perfect face

of the pseudoeffective cone, and I will determine its extermal rays.

Moreover, I will describe a series of cones related to the contractibility properties

of the Abel-Jacobi morphism, which form a maximal chain of perfect faces of

the pseudoeffective cone, provided that $C$ is a very general curve and $d$

is sufficiently large. This is a joint work with A. Kouvidakis, A.F. Lopez and F. Viviani.

M. BOLOGNESI :

Title: A variation on a theme of Faber and Fulton

Abstract : In this talk we study the geometry of GIT congurations of n ordered points on P1 both
from the the birational and the biregular viewpoint. In particular, we prove that any extremal ray of
the Mori cone of effective curves of the quotient (P1)^n//PGL(2), taken with the symmetric polarization,
is generated by a one dimensional boundary stratum of the moduli space. Furthermore, we develop
some technical machinery that we use to compute its group of automorphisms. (joint work with A.Massarenti)



F. CAMPANA :

Title: Dense entire curves in rationally connected manifolds

Abstract : we show in particular that for any given sequence of points on a rationally

connected manifold X, there is a holomorphic map from the complex line to X

whose image contains all these points. (Joint with Joerg Winkelmann)

L. EIN 

Title : Singularities and syzygies of secant varieties of curves I

A. KURONYA :

Title : Effective global generation on manifolds with numerically trivial canonical bundle
Abstract : If L is a line bundle on a projective manifold, then the
existence of effective bounds for its tensor powers to have global
sections or become globally generated have been a central problem in
algebaic geometry for the last 150 years. While the case of curves
follows from Riemann-Roch, satsifactory answers for surfaces only
arrived about thirty years ago. Research in the area has been mostly
motivated by Fujita's conjectures predicting the global generation and
very ampleness of certain adjoint line bundles. In this talk we will
consider the case of effective global generation for projective
manifolds with numerically trivial canonical bundle. This is an
account
of joint work with Yusuf Mustopa.

J. LIU :

Title: Manifolds admitting locally rigid hypersurfaces as ample divisors

Abstract: Polarized manifolds containing special subvarieties

as ample divisors are fundamental objects in adjunction theory.

In this talk I will focus on the polarized pairs $(X,A)$

where $A$ is a locally rigid smooth Fano hypersurface

of a rational homogeneous space $G/P$ of Picard number

one and show how the VMRT theory gives a classification of such pairs.

A.F. LOPEZ :

Title: On the existence of Ulrich vector bundles on some irregular surfaces
Abstract: The problem of existence of Ulrich vector bundles is open already in  
the case of surfaces. In the talk we will outline the existence of  
rank two Ulrich vector bundles on surfaces that are either of maximal  
Albanese dimension or with irregularity $1$, under many embeddings. In  
particular this gives the first known examples of Ulrich vector  
bundles on irregular surfaces of general type.

W. NAHM :

J. CH. OTTEM :

Title: Deformations of hypersurfaces

Abstract: I will discuss an old question due to Kollár and Mori: when is a smooth specialization of


a family of hypersurfaces again a hypersurface? This is joint work with Stefan Schreieder.



G. PACIENZA :

Title: On the cone conjecture for singular irreducible holomorphic symplectic varieties. 


Abstract: I will report on a joint work in progress with Ch. Lehn and G. Mongardi in which we explore

the possibility of extending the Kawamata-Morrison cone conjecture to singular irreducible holomorphic symplectic varieties.

The conjecture for smooth IHS varieties was recently established by Amerik-Verbitsky, based upon previous works due to Markman, Markman-Yoshioka, 

and Amerik-Verbitsky. 



G. PARESCHI :

Title: Inequalities for coherent sheaves and divisors on abelian
varieties

Abstract: I will discuss some old and new lower bounds for the Euler
characteristic of coherent sheaves on abelian varieties satisfying
certain vanishing conditions. An application of them is the proof of a
conjecture of O. Debarre and Ch. Hacon on singularities of divisors of

low degree on simple abelian varieties.
J. PARK :

Title: Singularities and syzygies of secant varieties of curves II

Abstract: This talk is a continuation of Lawrence Ein's talk. We consider the k-th

secant variety of a smooth projective complex curve of any genus embedded by the

complete linear system of a very ample line bundle of high degree. I give a sketch of the

proofs of the following results: (1) The k-th secant variety has mild singularities naturally

appearing in birational geometry. (2) The k-th secant variety is arithmetically

Cohen-Macaulay, and satisfies the N_{k+2,p}-property. One of the main technical

ingredients is a vanishing theorem on Cartesian product of curves. This talk is based on

joint work with Lawrence Ein and Wenbo Niu.



J. ROE :

Title : Squeezing the juice out of Newton-Okounokov bodies

Abstract : Since the formalization of Newton-Okounkouv bodies by Kaveh-Khovanski

and Lazarsfeld-Mustata about ten years ago, we have learned a lot about their shape and

how it reflects the properties of varieties and line bundles, espcially concerning

cohomology and positivity. After Jow’s proof that the set of all Newton-Okounkov bodies

of a given line bundle is a complete numerical invariant (and local variants of this result)

it is natural to ask about this set, for instance, how do bodies of a given line bundle vary

by chosing different flags/valuations ? And how can one extract information about the line

bundle from its collection od bodies ? I will look at some well known results on Newton-Okounkov

bodies from this point of view, and report on work in progress with Moyano-Fernàndez,

Nickel and Szemberg for the case surfaces and Newton-Okounkov polygons.

E. ROUSSEAU :

Title :Symmetries of transversely projective foliations

Abstract:  Algebraic curves with positive canonical line bundle are known to have

finitely many automorphisms. In a joint work with F. Lo Bianco, J.V. Pereira, and F.

Touzet, we look for foliated versions of this classical fact. Such generalizations are

obtained on projective manifolds for transversely hyperbolic foliations and more generally

for transversely projective ones, whereas some counter-examples are given for non Kähler

manifolds. This study also provides interesting consequences for the distribution of entire

curves on manifolds equipped with such foliations.


T. SZEMBERG 

Title: Postulation in projective spaces and unexpected hypersurfaces

Abstract:

Given a suscheme X in projective space, it is very classical problem to determine the

dimension of the vector space of all homogeneous polynomials of some fixed degree d

vanishing along X. Even in the simplest case, when X is supported on finite set of points

in the projective plane , a complete answer is not known and it is subject to open

conjectures due to Nagata (1959) and Segre-Harbourne-Gimiliano-Hirshowitz (1964-78).

Recently Cook II, Harbourne,Miliore and nagel observed that the situation becomes even

more interesting if one replaces the space of all polynomials of certain degree by its

carfully chosen subspaces, I will focus on examples exhibiting these new phenomena.

This is based on joint work with Bauer, Malara and Szpond.

J. SZPOND :

Title: Unexpected curves and Togliatti-type  surface

Abstract: I will report on a recent work on a direct link between the theory of

unexpected hypersurfaces and varieties with defective osculating behavior.

For a smooth, complex projective variety X embedded in a projective

space, and a positive integer m, one defines the m-th osculating space

to X at P as the linear subspace determined at a point P by the partial

derivatives of order less then or equal to m of coordinate functions,

with respect to a system of local parameters for X at P, evaluated at P.

If the dimension of the m-th osculating space at a general (hence any)

point P of X is lower than expected (hence certain cohomology group is

not vanishing) then X is said to be hypo-osculating of order m.

Recently Cook II, Harbourne, Migliore and Nagel introduced the notion

of unexpected hypersurfaces. In the simplest case, we say that a finite

set of points Z in the projective plane admits in a general point P an

unexpected curve C of degree d and multiplicity m at P, if the existence

of C does not follow from a naive dimension count (i.e. again a certain

cohomology group is not vanishing).In my talk I will discuss how these two

phenomena are related to each other. This will be illustrated by an example

attached to the B3 root system.