Monday, May 30

Tuesday, May 31

Wednesday, June 1






9h1510h15

Damon 
9h1510h15

Matei 




* 
café

* 
café





10h4011h40

Stevens

10h4011h40

Parameswaran

14h0015:00

Siersma 
14h0015:00

Maxim


*

café

* 
café


16h3017h30

FrühbisKrüger

15h3016h30

Budur


17h4518:45 
Zach 
16h4517h45

..... 
Arnaud Bodin (Lille) Nero Budur (Leuven) Octave Curmi (Lille) James Damon (Chapel Hill) Anne FrühbisKrüger (Hannover) Laurentiu Maxim (Bonn) Daniel Matei (Bucuresti) A.J. Parameswaran (Mumbai) Youssef Hantout (Lille) 
Patrick PopescuPampu (Lille) Dirk Siersma (Utrecht) Jan Stevens (Göteborg) Yongqiang Liu (Leuven) Mihai Tibar (Lille) Matthias Zach (Hannover) 
Laurentiu Maxim Characteristic classes of singular complex hypersurfaces
Abstract.
An
old problem in geometry and topology is the computation of
topological and analytical invariants of complex hypersurfaces, e.g.
Betti numbers, Euler characteristic, signature, HodgeDeligne
numbers, etc...
While the nonsingular case is easier to deal with, the
singular setting requires a subtle analysis of the intricate relation
between the local and global topological and/or analytical structure
of singularities.
In this talk I will explain how to compute
characteristic classes of complex hypersurfaces in terms of local
invariants of singularities.
This is joint work with S. Cappell, M.
Saito, J. Schuermann and J. Shaneson.
James Damon Topology of Exceptional Orbit Hypersurfaces of Prehomogeneous Spaces
Abstract.
We consider the topology for a class of hypersurfaces with
highly nonisolated singularites which arise as “exceptional orbit
varieties” of a
special class of prehomogeneous vector spaces, which are
representations of linear algebraic groups with open orbits.
These hypersurface
singularities include both determinantal hypersurfaces and linear free
(and free*) divisors.
Although these hypersurfaces have highly
nonisolated singularities, we determine the topology of their Milnor
fibers, complements and links.
We do so by using the action of
linear algebraic groups beginning with the complement, instead of using
Morsetype arguments on the Milnor fibers.
This includes
replacing the local Milnor fiber by a global Milnor fiber which has a
“complex geometry” resulting from a transitive action of an appropriate
algebraic group, yielding a compact “model submanifold” for the
homotopy type of the Milnor fiber.
Unlike isolated singularities, the cohomology of the Milnor
fibers and complements are isomorphic as algebras to exterior algebras or
for one family, modules over exterior algebras; and cohomology of the
link is, as a vector space, a truncated and shifted exterior algebra, for
which the cohomology product structure is essentially trivial.
We also
deduce from Bott’s periodicity theorem, the homotopy groups of the Milnor
fibers for determinantal hypersurfaces in the “stable range”.
Dirk Siersma Milnor fibre homology via deformation
Abstract
We study hypersurfaces of dimension n with a 1dimensional singular
set and consider admissible deformations for the study of the Milnor
fibre.
It’s homology depends very much on the types of special singularities in the deformation.
In dimension n1 there are strong bounds related to the minimum of the n1 Betti numbers of the special fibres.
In several cases we can even show that the homology is concentrated in dimension n only.
The same technique has been used by us to compute the vanishing
homology of projective hypersurfaces with a1dimensional singular set.
This is joint work with Mihai Tibar (two titles on arXiv).
Daniel Matei Real Arrangements and Contact Structures
Abstract
We consider contact structures that appear in connection with
singularities of polynomial mappings through the notion of open bo! ok
decompositions.
For real singularities that arise from arrangements of real subspaces,
we analyze the range of possible contact structures, from the
perspective of the dichotomy tight versus overtwisted, highlighting the
tightness restrictions of the holomorphic case. This is joint work with
M. Tibar.
Matthias Zach The Topology of Isolated CohenMacaualy codimension 2 Singularities
Abstract
A matrix singularity $(X,0)\subset (C^N,0)$ is a complex space
germ whose ideal $I$ is generated by minors of a matrix $M$ with polynomial (resp. analytic) entries.
Those singularities in the title, abbreviated as ICMCd2singularities,
fall into this category. As in the case of complete intersection singularities deformations
of $(X,0)$ can easily be described and if $(X,0)$ admits a smoothing,
one can ask for the topology of the smooth fiber.
We have recently described the Tjurina modification for
ICMCd2singularities, which in case of CohenMacaulaytype 2 translates
the problem to a local complete intersections scheme. However, this
comes at the cost of possibly having a onedimensional singular locus.
I will discuss how to apply old and recent results about the latter singularities to tackle the topology of matrix singularities.
Nero Budur Cohomology support loci
Abstract
Cohomology support loci are homotopy invariants of topological spaces.
For complex varieties, they encode a rich part of the geometry of the
variety.
These loci are notoriously difficult to compute.
We will
present two recent advances in this direction. One is due to joint
work with LiuSaumellWang and provides an A'Campo type formula.
The
other is due to Maisonobe who proved a big part of some of our
conjectures on BernsteinSato ideals.
A.J.Parameswaran On mixed functions of type $f\bar g$
Abstract.
Let $f$, $g$ be two holomorphic function germs. The study of the class of functions $f\bar g$ produced many results.
Here we study the Thom regularity of $f\bar g$
This is a joint work with Mihai Tibar.
Jan Stevens Improvements of nonisolated surface singularities
Abstract
Anne FrühbisKrüger An Algorithm for Computing the Discriminant of Families of Essentially Isolated Determinantal Singularities (EIDS)
Abstract
The compuation of the discriminant of a family of singularities is a
computationally expensive task, because it requires a Groebner basis
computation of an ideal of minors with respect to an elimination
ordering. In many relevant cases, the computation is not feasible due
to the complexity of the result.
For families of EIDS, however, the
special structure of the equations can be used to apply a divide and
conquer approach to the problem. As a byproduct, this approach
provides a meaningful decomposition of the discriminant.
In this talk,
I shall explain this approach in detail.