10 mai 2017

 
Remise des Palmes Académiques à Thierry Ramond

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Résumé : Thierry Ramond sera décoré des palmes académiques pour services éminents rendus à l’Education Nationale. Un pot festif aura lieu à cette occasion. Félicitations Thierry !
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Remise des Palmes Académiques à Thierry Ramond  Version PDF

Wei Guo Foo (Orsay)
Explicit calculation of Siu’s Effective Termination in Kohn’s Algorithm for Special Domains in C^{3}

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Lieu : Salle 113-115

Résumé : We follow the arguments in a paper of Y-T. Siu to study the effective termination of Kohn’s algorithm for special domains in \mathbb{C}^{3}. We make explicit the effective constants and generic conditions that appear there, and we obtain an explicit expression for the regularity of the Dolbeault laplacian for the \overline{\partial}-Neumann problem. Specifically, on a local
peudoconvex domain of the special shape
\[<br class='autobr' />\Omega:=<br
class='autobr' />\bigg\{(z_{1},z_{2},z_{3})\in\mathbb{C}^{3}:\ <br
class='autobr' />2\text{Re}\ z_{3}+<br
class='autobr' />\sum_{i=1}^{\NN}|F_{i}(z_{1},z_{2})|^{2}<0<br
class='autobr' />\bigg\}<br
class='autobr' />\]<br
class='autobr' />with holomorphic function germs F_1,\dots,F_\NN\in\mathcalO_\mathbbC^2,0 of finite intersection multiplicity<br class='autobr' />\[<br
class='autobr' />s:=\dimsmall_{\mathbb{C}}\ <br
class='autobr' />\mathcal{O}_{\mathbb{C}^{2},0}<br
class='autobr' />\big/<br
class='autobr' />\langle <br
class='autobr' />F_{1},\dots, F_{\NN}<br
class='autobr' />\rangle<br
class='autobr' /><<br
class='autobr' />\infty,<br
class='autobr' />\]<br
class='autobr' />we show that an \varepsilon-subelliptic regularity for (0,1)-forms holds whenever, just in terms of s,<br class='autobr' />\[<br
class='autobr' />\varepsilon<br
class='autobr' />\geqslant <br
class='autobr' />\frac{1}{<br
class='autobr' />2^{(4s^{2}-1)s+3}<br
class='autobr' />s^{2}(4s^{2}-1)^{4}<br
class='autobr' />\binom{8s+1}{8s-1}}.<br
class='autobr' />\]

Explicit calculation of Siu’s Effective Termination in Kohn’s Algorithm for Special Domains in C^{3}  Version PDF

mai 2017 :

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