list of talks

 

 
Home
List of Talks
Program
List of Participants
Related activities
Practical infos
Contact
 

Norbert A'Campo
"Courbes de reduction de la monodromie et cycles quadratiques evanescents"
Résumé: On construit pour la fibre de Milnor d'une singularité isolée de courbe plane un model (F,\Sigma,\Delta), qui montre sur la surface à bord F le système de reduction \Sigma de la monodromie géométrique et un système distingué de cycles évanescents quadratiques \Delta. Le système \Sigma est une famille de courbes simples sur F, deux à deux disjointes, qui est invariante par la monodromie géométrique. Une application concernant les groupes de monodromie homologique ou géométrique est donnée.


Edward Bierstone
"Algorithmes de desingularisation"
Résumé: On compare quelques algorithmes récents de désingularisation canonique, en terme de la dépendance des invariants locaux en fonction des diviseurs exceptionnels. Exemple: désingularisation des variétés toriques (ou localement binomiales).


Jean-Paul Brasselet
"Nombres et classes de Milnor"
Résumé: Il existe plusieurs notions d'indices de champs de vecteurs ayant des singularités (isolées) en les singularités isolées d'hypersurfaces. En particulier, la différence entre le "GSV"-indice et l'indice "classique" (de Poincaré-Hopf) s'exprime en fonction du nombre de Milnor. La généralisation de ce resultat est une expression géométrique de la différence entre classe de Schwartz-MacPherson et classe de Fulton-Johnson, dans le cas d'intersections completes.


Helmut Hamm
"Théorèmes de Lefschetz : théorie de Morse et pinceaux de Lefschetz"
Résumé: Pour la démonstration du théorème classique de Lefschetz sur les sections hyperplanes, on peut ou bien utiliser la théorie de Morse (Andreotti-Frankel) ou bien des pinceaux de Lefschetz. On va comparer les deux méthodes et leur comportement par rapport aux généralisations.


Claus Hertling
"Primitive forms, Frobenius manifolds, and moduli of singularities"
Abstract: The construction of Frobenius manifolds in singularity theory is based on K. Saito's primitive forms and results of M. Saito. As an application I can show the existence of global moduli spaces for the singularities in one mu-homotopy class. The construction and this application will both be sketched. I also intend to give an idea of the relation to topics as Gauss-Manin connections, isomonodromic deformations, mixed Hodge structures, versal Lagrange maps, free divisors.


Anatoly Libgober
"Elliptic genus of toric varieties."
Abstract: I will discuss two variable elliptic genus for toric varieties or hypersurfaces in toric varieties with Gorenstein singularities as well as a relationship between elliptic genera of hypersurfaces which are mirrors of each other (joint work with L.Borisov).


Mutsuo Oka
"Elliptic curves from sextics."
Abstract: Let N be the moduli space of sextics with 3 (3,4)-cusps. The quotient moduli space N/G is one-dimensional and consists of two components, N_{torus}/G and N_{gen}/G. By quadratic transformations, they are transformed into one-parameter families C_s and D_s of cubic curves respectively. First we study the geometry of N_\eps/G, where \eps = torus or gen, and their structure of elliptic fibration. Then we study the Mordell-Weil torsion groups of cubic curves C_s over Q and D_s over Q(\sqrt{-3}) respectively. We show that C_s has the torsion group Z/3Z for a generic s in Q and it also contains subfamilies which coincide with the universal families given by Kubert with the torsion groups Z/6Z, Z/6Z + Z/2Z, Z/9Z or Z/12Z. The cubic curves D_s have torsion Z/3Z + Z/3Z generically but also Z/3Z + Z/6Z for a subfamily which is parametrized by Q(\sqrt{-3}).


Dirk Siersma
"Embeddings of smooth lines into hypersurfaces."
Abstract: We use singularity theory in order to study the positions of smooth lines in singular hypersurfaces. Sometimes many positions are possible, but in some case they don't exist. We define invariants, related to the relative position, study Morsification and monodromy.


David Trotman
"Stratified transversality via isotopy."
Abstract: For X a (w)-regular or (c)-regular stratification, hence for any Whitney stratification and, via regular embedding, for any abstract stratified set, we give an extension theorem for diffeomorphisms defined on strata of a given dimension. Then we show that after isotopy a stratified subspace W of X can be made transverse to a stratified map $ g: Y \to X$, and study cases where the isotopy preserves regularity of W. There are applications to the homology theory of stratified sets extending work of Goresky and Murolo.


Home | List of Talks | Program | List of Participants |Related activities | Practical infos | Contact