CIMPA
SCHOOL SCHEDULE

Monday 14

Tuesday 15

Wedns. 16

Thursday 17

Friday 18

Satur. 19

Monday 21

9:0010:15 
Registration / Coffee

GomezMont 2

Artal 3

GomezMont 3

Dimca 4

Nemethi 3

Nemethi 4

10:1510:30 
Break 
Break 
Break

Break

Break

Break

Break

10:3011:45 
GomezMont 1

Artal 2 
Dimca 2

Dimca 3

Artal 4

Veys 3

Veys 4

11:4512:30 
Coffee break

Coffee break 
Coffee break

Coffee break

Coffee break

Coffee break

Coffee break

12:3013:45 
Artal 1

Nemethi 1

Nemethi 2

Veys 1

Veys 2

GomezMont 4

Talk D. Kerner. 
Lunch








16:0017:15 
Dimca 1

Talk M. Pe /S. Martinez 
Dimca Exe 
Talk D.S. Kumar 
Talk H. Cobo / E. Gorsky 
Free

Talk
L. Maxim 
17:3018:20 
Talk A. Campillo

GomezMont Exer. 
Artal Exer.

Talk P. Petrov

Nemethi Exer. 
Free

Talk Pi. CassouNogues 
Abstracts for talks
Evgeny Gorsky: "Motivic integrals and functional equations"
Abstract: A functional equation for the motivic integral corresponding
to the Milnor
number of an arc is derived using the DenefLoeser formula for the
change of variables. Its solution is a function of five auxiliary
parameters, it is unique up to multiplication by a constant and there
is a
simple recursive algorithm to find its coefficients.
The method is universal enough and gives,
for example, equations for the integral corresponding to the
intersection
number over the space of unordered tuples of arcs.
Dmitry Kerner: "Enumeration of
unisingular plane curves / hypersurfaces"
Abstract: We enumerate complex algebraic hypersurfaces in $P^n$, of a
given (high) degree with one singular point of a given singularity
type. Our approach is to compute the (co)homology classes of the
corresponding equisingular strata in the parameter space of
hypersurfaces. We suggest an inductive procedure, based on the
classical intersection theory combined with liftings (partial
resolutions) and degenerations. The procedure computes the (co)homology
class in question, whenever a given singularity type is properly
defined. We will start from enumeration of unisingular plane curves
(in this case
the method is particularly simple and is applicable to any singularity
type).
If time permit we will consider the case of hypersurfaces. Here we
restrict consideration to the generalized Newtonnondegenerate
singularities.
Shiv Datt Kumar: "Sections of Zero
Dimensional Ideals Over a Notherian Ring".
Abstract: Let $A$ be a commutative Noetherian ring and $I \subset A[T]$
be an ideal containing a monic polynomial such that $A[T]/I$ is a zero
dimensional. Suppose conormal module $I/I^{2}$ is generated by $r$
elements over $A[T]/I$. Then a set of $r$ generators of $I(0) : = \{
f(0) f \in I \}$ can be lifted to a $r$ generating set of $I$.
Sergio Martinez: "Algorithmic
computation of local braid monodromy for plane singularities"
Abstract: Braid monodromy provides a complete description of the
topology of plane
algebraic curves. The simplest case is the study of local singularities
of
plane curves. In this situation a single braid is enough to describe
their
braid monodromy and such a braid encodes the complete topological
information because its closure is the link associated with the
singularity
Laurentiu Maxim: "Genera of
complex varieties and singularities of proper maps"
Abstract: I will report on recent work (jointly with S. Cappell and
J.Shaneson) on Hodgetheoretic genera of (possibly singular) projective
varieties. These are oneparameter families of invariants extending to
the singular setting the classical Hirzebruch genera of Kahler
manifolds,
and including as a particular case the GoreskyMacPherson signature of
a
complete variety. I will present formulae that relate these global
invariants of a projective variety X to such invariants of
singularities
of proper algebraic maps defined on X. Such formulae severely
constrain,
both topologically and analytically, the singularities of complex
maps,even between smooth varieties.
Maria Pe Pereira "On equisingularity of parametrised surfaces"
Abstract: (Joint work with J. Fernandez de Bobadilla) Let
$f_t:(\mathbf{C}^3,O)\to \mathbf{C}$ be a family of reduced holomorphic
germs. We say that $f_t$ is {\em equisingular at the normalisation} if
the pairs given by the topological normalisation of the zero set of
$f_t$ and the inverse image by the normalisation map of the singular
set of $f_t^{1}(0)$ form a topologically equisingular family. We prove
that, if L\^e's conjecture holds, equisingularity at the normalisation
is equivalent to topological rightequisingularity for the family
$f_t$. Furthermore, if the generic transversal type of the
singularities of $f_t$ are curve singularities with smooth branches
then the statement does not depend on L\^e's conjecture.
The case in which the above result is most meaningful is the case of
parametrised surfaces. Let $h_t:(\mathbf{C}^2,O)\to (\mathbf{C}^3,O)$
be a family of finite and generically $11$ holomorphic germs depending
holomorphically on a parameter $t$. Assuming L\^e's conjecture we prove
that the family is topologically $A$equisingular if and only if the
Milnor number of the curve given by the inverse image by $h_t$ of the
critical set of $h_t(\mathbf{C}^2)$ is constant. The result is
independent on L\^e's conjecture in the case of finitely $A$determined
map germs. Thus we obtain as a particular case a recent result of
CallejaBedregal, Ruas and Houston. We also prove that if the generic
L\^e numbers at the origin of $h_t(\mathbf{C}^2)$ are independent on
$t$ then the family is topologically $A$equisingular.
Similar results are obtained for the case of a family of maps
\[h_t:(V,O)\to (\mathbf{C}^3,O),\]
where $(V,O)$ is a normal surface germ.