Tel Aviv University
 
Hello everyone,
 
The next colloquium talk will be held on Monday, 2/1/2012, 12:15, Schreiber
006, Tel Aviv University.
The speaker is
 
    Dmitry Kerner (University of Toronto)
 
and the title of his talk is
 
    Local geometry of singular varieties
 
The abstract is given below. Tea and coffee at 12:00, same room.
 
Hope to see you there. For information about future colloqiua, see
 <http://www.math.tau.ac.il/~klartagb/colloq_2011.html>
You are all welcome to suggest colloquium speakers for the second semester,
and also for January 30th.
 
Yours,
Bo'az
 
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Abstract: Singular varieties occur everywhere. Two natural ways to study
them are to deform (to smoothen) or to resolve the singularities. It is
natural to compare the invariants of the singular variety and of its smooth
fellows. This defines various invariants of singular varieties.
 
The fundamental topological invariant is the Milnor number (the defect of
the topological Euler characteristic). The fundamental geometric invariant
is the singularity genus (the defect of the holomorphic Euler
characteristic). An old conjecture, [Durfee 1978], bounds the singularity
genus in terms of the Milnor number.
 
I will start from the general introduction to non-smooth varieties and then
proceed to the recent advances in the study of these invariants. Jointly
with A.Nemethi, we constructed series of counterexamples, violating the
conjecture, even asymptotically. Further, we succeeded to formulate a
corrected version, which is asymptotically sharp, and proved this version
for a big class of singularities.
 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Bo'az Klartag   <klartagb@post.tau.ac.il>