non-mobile-version | mobile-version |

Gavril Farkas | Bruno Klingler |

## RegistrationFor registration please use the webform. ## Participantsfull list of participants (last update: Thu, 16.11.2017 09:53:02) ## Programme
## Abstracts Marian Aprodu — I report on a joint work in progress with G. Farkas, S. Papadima, C.
Raicu and J. Weyman. Koszul modules are multi-linear algebra objects
associated to an arbitrary subspace in a second exterior power. They are
naturally presented as graded pieces of some Tor-s over the dual
exterior algebra. Koszul modules appear in the Geometric Group Theory,
in relations with Alexander invariants of groups. We prove an optimal
vanishing result for the Koszul modules, and we describe explicitly the
locus corresponding to Koszul modules that are not of finite length. To
this end, we produce and verify a degenerate version of Green’s
conjecture that holds for cuspidal curves and we use representation
theory to connect the syzygies of rational cuspidal curves to some
appropriate Koszul modules, called Weyman modules. We apply our
vanishing result to Alexander invariants. Sebastian Casalaina-Martin — Associating to a smooth cubic threefold its principally
polarized intermediate Jacobian induces a rational period map from the
GIT moduli space of cubic threefolds to the second Voronoi
compactification of the moduli space of five dimensional principally
polarized abelian varieties. In this talk I will describe a resolution
of the period map, which allows for a geometric description of the
boundary of the moduli space of intermediate Jacobians. This is joint
work with Samuel Grushevsky, Klaus Hulek, and Radu Laza. Thomas Krämer — To any holonomic D-module on an abelian variety one may attach an algebraic group via the Tannakian formalism of convolution. Applying this to the intersection homology D-module of a closed subvariety, one obtains a bridge between geometry and representation theory: The highest weight theory of the arising groups is related to geometric topics such as Gauss maps, subvarieties dominated by a product of varieties, singularities of theta divisors, the Schottky problem, second order theta functions etc. In this talk, I will report on recent progress concerning these relations. Victor Lozovanu — Seshadri constants measure the local positivity of an ample line bundle at a
fixed point. Due to this, they show up in many areas of mathematics ranging from Kähler
to algebraic or arithmetic geometry. In this talk I will try to explain how can one study
these invariants using convex geometry. As a consequence of these methods, thus having
local information, and singularity theory can lead to understanding of global properties on
abelian varieties in terms of data on abelian submanifolds. Mateusz Michalek — For a homogeneous polynomial $P$ it is a classical problem to understand its presentations as a sum of powers of linear forms $P=\sum_{i=1}^r l_i^r$. The smallest possible $r$ is known as the Waring rank of $P$. Over the reals, we may have a family of Euclidean open sets with consecutive Waring ranks. We will describe the geometry of these sets in special cases. Further, for a fixed $P$ we may have many Waring decompositions. Over the complex numbers their moduli - the Variety of Sums of Powers - has been studied by Mukai, Ranestad, Schreyer and others. The real decompositions correspond to a semialgebraic subset of the real part of the VSP. We will present several results concerning these subsets from a joint work with Moon, Sturmfels and Ventura. Simon Pepin Lehalleur — Following Grothendiecks vision that many cohomolgical
invariants of of an algebraic
variety should be captured by a common motive, Voevodsky
introduced a triangulated category of mixed motives which partially realises
this idea. After describing this category, I will explain how to
define the motive of certain algebraic stacks in this context. I will
then report on joint work in progress with Victoria Hoskins, in which
we study the motive of the moduli stack of vector bundles on a smooth
projective curve and show that this motive can be described in terms of
the motive of this curve and its symmetric powers. Michel van Garrel — Let X be a smooth projective variety and let D be a smooth nef divisor on it. In this collaboration with Tom Graber and Helge Ruddat, we show that the genus 0 local Gromov-Witten (GW) invariants of the total space of O(-D) equal, up to a factor, the genus 0 log GW invariants of X with a single condition of maximal contact order along D.## VenueThe lectures on the ## DinnerThere will be a dinner on Thursday evening at 19:00 at 12 Apostel Berlin Mitte. ## Hotels. |