[Vortraege] Vortrag H. Ruddat - Änderung Vortragsinhalt

[Danijela Radosavljevic]

  Sehr geehrte Fakultätsmitglieder,

anbei der geänderte Vortagsinhalt von H. Ruddat.

Mit freundlichen Grüßen

Danijela Radosavljevic
Sekretariat
Institut für Mathematik
Universität Wien
Nordbergstr. 15, UZA 4
Tel: 43 1 4277 50629
Fax: 43 1 4277 9506



Freitag, 18. März 2011, ab 14:00 Uhr, Seminarraum D 103, UZA 4
Vorträge
H. Ruddat:

Vortag, 14:00 Uhr
1. Griffiths reisdues and tropical realization Jacobian rings.

It was observed by Dwork and Griffiths that the
interesting part of the cohomology of a smooth ample hypersurface in
projective space is Hodge-graded isomorphic to the Jacobian ring of the 
defining polynomial.
The isomorphism is realized by a residue map from differentials on the 
affine complement of the
hypersurface. Jacobian rings also determine the cohomology of the Milnor 
fibre of an
isolated singularity. This is no coincidence since the affine cone over 
a smooth
hypersurface gives rise to an isolated singularity. Batyrev generalized 
Jacobian rings to
the situation where the projective space is replaced by a toric variety.
We review these notions, describe techniques to compute Jacobian rings and
give applications to mirror symmetry.

Vortrag, 15:30 Uhr
2.Mirror Symmetry partners via vanishing cycles

In a joint work with Mark Gross and Ludmil Katzarkov, we propose a
construction for mirror symmetry partners which works for any Kodaira 
dimension, e.g. this
allows us to produce the mirror of a complex curve of any genus. In 
general, the
mirror will be very singular and equipped with a sheaf of vanishing 
cycles. We
associate Hodge numbers to the singular space with this sheaf and show 
that these fulfil
the mirror duality h^{p,q}(X) = h^{d-p,q}(Y) for X,Y a d-dimensional 
mirror pair of
our construction.
In this talk, I intend to introduce the construction and demonstrate a few
examples.

organized by L. Katzarkov