[Vortraege] Nachtrag Vortragsankündigungen KW. 11

[Danijela Radosavljevic]

  Sehr geehrte Fakultätsmitglieder,

anbei ein Nachtrag der Vortragsankündigungen für diese Woche.

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:

1. Analogues of
Griffiths reisdues and tropical realization Griffith's residues and toric
Jacobian ringsIt was observed by Dwork and Griffith 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.

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



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