SMS scnews item created by Zhou Zhang at Mon 29 Jul 2013 1258
Type: Seminar
Modified: Tue 30 Jul 2013 2058
Distribution: World
Expiry: 19 Aug 2013
Calendar1: 1 Aug 2013 1200-1300
CalLoc1: Carslaw 707A
Auth: zhangou@como.maths.usyd.edu.au

GTA Seminar: Parusinski -- Introduction to Abhyankar-Jung Theorem

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.

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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.)

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Seminar website:

http://www.maths.usyd.edu.au/u/SemConf/Geometry/


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