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Programme

Mer. 29 Jeu. 30 Ven. 01

‹ jeudi 30 septembre 2021 ›

08:00

09:00

10:00

11:00

12:00

13:00

14:00

15:00

16:00

17:00

›8:30 (30min)

CAFE

›9:00 (50min)

S. TRIVEDI (via Zoom) : Transversality and its relation to regular stratifications in smooth, complex and o-minimal setting : Trotman in his Ph.D. thesis proved that the stability of transversality to a stratification implies Whitney (a)-regularity of the stratification. I will talk about a generalization of this result and also its analogues in the complex case and in o-minimal structures.

›9:50 (50min)

L. PAUNESCU (via Zoom) : ARC-WISE ANALYTIC STRATIFICATION, WHITNEY FIBERING CONJECTURE AND ZARISKI EQUISINGULARITY (with Adam Parusinski) : For a given germ of complex or real analytic set, we show the existence of a stratification satisfying a strong (real arc-analytic with respect to all variables and analytic with respect to the parameter space) trivialization property along each stratum. We call such a trivialization arc-wise analytic and we show that it can be constructed under the classical Zariski algebro-geometric equisingularity assumptions. Using a slightly stronger version of the Zariski equisingularity, we show the existence of Whitney’s stratified fibration, satisfying the conditions (b) of Whitney and (w) of Verdier. Our construction is based on the Puiseux with parameter theorem and a generalization of Whitney’s interpolation. For algebraic sets our construction gives a global stratification.

›10:40 (20min)

CAFE

›11:00 (50min)

K. KURDYKA (à la FRUMAM) : Subanalytic curve-analytic function is actually analytic: A function is called curve-analytic, if for any germ of analytic curve its restriction coincides with restriction of some analytic function. It turns out that this property with assumption that the graph is subanalytic implies that the function is analytic. Joint work with W. Kucharz.

›11:50 (2h10)

DEJEUNER

›14:00 (50min)

T. GAFFNEY (à la Frumam): The theory of integral closure and C, B, \delta and A_f : The theory of stratifications is a central strand in David Trotman’s work. With his collaborators and students he has contributed to our understanding of Whitney’s conditions A and B, condition C, initiated the study of condition delta and introduced the weak Whitney conditions. The theory of the integral closure of modules provides ways to understand these conditions, the relations between them and the relation between infinitesimal and local phenomena. I will illustrate this in my talk using Whitney B, various strengthenings of the condition M introduced by Bekka and Koike, Condition delta and the Weak Whitney conditions. This is a report on work from a current project with Leslie Wilson.

›14:50 (50min)

PARUSINSKI : Algebraic Stratified General Position and Transversality : We use the method of Whitney interpolation to construct, for any real or complex projective algebraic variety, a stratified submersive family of self-maps that yields stratified general position and transversality theorems for semialgebraic chains. This theorem can be used to define an intersection pairing for real intersection homology, an analog of intersection homology for real algebraic varieties. Based on joint works with Clint McCrory and Laurentiu Paunescu.

›15:40 (30min)

CAFE

›16:10 (50min)

C. McCRORY (via ZOOM) : The intrinsic stratification of a semialgebraic set : Shiota’s semialgebraic Hauptvermutung and methods of PL topology are used to investigate semialgebraically locally trivial stratifications.

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Discours

Logistique

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