M.-H. Nicole

Marc-Hubert Nicole (Marseille)

"Conjectures de troncature de Traverso et raffinements de la
stratification de Newton"

Thursday, March 3, 2011
 room 2BC60 – 14:00

ABSTRACT: Vers 1979, C. Traverso conjectura l'existence de bornes
universelles surprenamment petites pour déterminer un groupe de
Barsotti-Tate à isomorphisme près (resp. isogénie près) à partir de ses
groupes de Barsotti-Tate tronqués d'échelon n. La conjecture d'isogénie
fut prouvée par le conférencier et A. Vasiu en 2006 de manière
élémentaire. Dans cet exposé, nous parlerons de la conjecture
d'isomorphisme. Nous remplacerons la borne originale de Traverso par une
borne correcte et optimale (dans un sens précis). En particulier, cette
conjecture de Traverso est vraie quand la codimension du groupe de
Barsotti-Tate est égale à sa dimension (exemple primordial: le groupe de
Barsotti-Tate d'une variété abélienne). Nous décrirons aussi la
variation en famille des invariants qui apparaissent naturellement dans
la résolution de ces conjectures, et qui donnent lieu à des
stratifications naturelles des strates [sic] de Newton. Travail en
commun avec E. Lau et A. Vasiu.

RICCI

SEMINARIO MATEMATICO E FISICO DI MILANO

AVVISO DI CONFERENZA

Venerdi' 25 febbraio 2010, alle ore 11:00
presso la Sala Consiglio VII piano del Dipartimento di Matematica, Politecnico di Milano,
in via Bonardi 9

Prof. FULVIO RICCI
Scuola Normale Superiore di Pisa

parlera'su

"Recenti sviluppi nella teoria degli integrali singolari"

Abstract: La teoria degli integrali singolari si e' sviluppata a partire dagli anni '50, as opera di Calderon e Zygmund, come strumento per l'analisi della regolarita' L^p di soluzioni di equazioni ellittiche, e al tempo stesso incorporando metodi, nati con Hilbert, Riesz, Hardy e Littlewood, nell'ambito dell'analisi complessa in una variabile. Nel corso degli anni, la teoria ha visto significativi ampliamenti, raffinamenti e sistematizzazioni, con un forte impatto in diversi ambiti dell'analisi. Verranno presentati alcuni recenti sviluppi della teoria, in un contesto motivato da problemi di analisi complessa in piu' variabili e teoria degli operatori ipoellittici.

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Tutti gli interessati sono invitati a partecipare.

Il direttore del Seminario
Franco Tomarelli

Per ulteriori informazioni sulle attività del seminario: http://www.mate.polimi.it/smf

seminario 24/2

Il giorno giovedi' 24 Febbraio
ore 14:30 Aula 5

Il dott. Alexandre Kirilov
(Dipartimento di Matematica ed Informatica, Università di Cagliari)

terrà un seminario su

"Global regularity and global solvability for smooth vector fields on S3"

Abstract:
The main goal of this work is to address  global properties  for classes of smooth (non)singular vector fields on S3. It is known that on S3 no C^infty globally hypoelliptic (GH) and no C^infty globally solvable (cohomologically free (CF) in the sense of Katok) vector fields exist.

First we consider classes of vector fields with one or two cycles which are attractors for all other integral curves. We show that the cohomological equation Lu=f, fin C^infty (S3) has at least one C^infty solution defined on S3 except the attractors and we can extend the soluion as a weak L1 function near the attractors. Moreover, we describe completely the propagation of singularities of all solutions u. As a particular case, we exhibit explicit vector fields whose integral curves coincied with  the foliations obtained by transversal intersection of linear holomorphic flows in C2  with S3 under nondegeneracy conditions.

Secondly, for a class of nonsingular vector fields which are invariant on the fibers (two dimensional tori) in “generalized solid tori" foliations of S3, we derive necessary and sufficient conditions for partial C^infty GH and partial C^infty GS  with respect to the fibers. We point out that our construction of solid tori yields novel family of 2D tori shrinking to cycles at the end points, different from the Clifford and Lwoson tori.

Moreover, the integral curves of the vector field correspond to foliations obtained by intersection of linear holomorphic flows with
degeneracies in the Poincare' domain.

We provide also results on the global solvability for more general classes of smooth vector fields (admitting also singular points) associated in a natural way to intersection of  linear C holomorphic flows and linear R2 actions on S3. In particular, we are able to classify completely the global properties of the cohomological equation  Lu =f on S3, provided L is obtained by foliations of linear holomorphic C or linear R2 actions.

[Joint work with A.Bergamasco and T. Gramchev]