Type: Seminar

Modified: Tue 30 Jul 2013 2058

Distribution: World

Expiry: 19 Aug 2013

Auth: zhangou@como.maths.usyd.edu.au

Speaker: Prof. Adam Parusinski (Nice) http://math.unice.fr/~parus/ Time: Thursday, August 1, 12NOON--1PM Room: Carslaw 707A Lunch: after the talk, at Law Annex Cafe. ---------------------------------------------- Title: Introduction to Abhyankar-Jung Theorem Abstract: Abhyankar-Jung Theorem is a multivariable generalization of Newton-Puiseux Theorem. It says that the roots of a polynomial $P(Z) = Z^d+a_1 (X) Z^{d-1}+ . . . +a_d(X)$, where $a_i (X)$ are complex analytic function germs of many complex variables $X=(X_1, …,X_n)$, are convergent fractional (i.e. with positive rational exponents) power series, provided the discriminant of $P$ is a monomial in $X$ times an analytic unit. A similar statement holds for formal power series over an algebraically closed field $K$ of characteristic zero. In this talk we give also a constructive proof of the latter statement by completing an old proof of Luengo. Our method can be applied to any Henselian local subring of $K[[X]]$ in particular to the quasi-analytic functions. (This is joint work with Guillaume Rond from Marseille.) ---------------------------------------------- Seminar website: http://www.maths.usyd.edu.au/u/SemConf/Geometry/