Type: Seminar

Distribution: World

Expiry: 1 Jun 2012

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

As requested by the audience regarding the rush of the previous talk (at least for the last 15 minutes or so), Prof. Milman has agreed to give a second talk next week, elaborating some important ideas. --------------------------------------------------- Speaker: Prof. Pierre Milman (University of Toronto) http://en.wikipedia.org/wiki/Pierre_Milman http://www.math.toronto.edu/cms/milman-pierre/ Time: Tuesday, May 15, 12(NOON)--1PM Room: Carslaw 352 Lunch: after the talk (at Taste at Sydney Uni, i.e. "Law School Annex Cafe") --------------------------------------------------- Title: Nash Desingularization for Binomial Varieties as Euclidean Multidimensional Division (joint work with Dima Grigoriev) Abstract: we establish a (novel for desingularization algorithms) apriori bound on the length of resolution of singularities by means of the composites of normalizations with Nash blowings up, albeit that only for affine binomial varieties of (essential) dimension 2. Contrary to a common belief the latter algorithm turns out to be of a very small complexity (in fact polynomial). To that end we prove a structure theorem for binomial varieties and, consequently, the equivalence of the Nash algorithm to a combinatorial algorithm that resembles Euclidean division (including in dimension>1) and, perhaps, makes Nash termination conjecture of the Nash algorithm particularly interesting. --------------------------------------------------- Web site for Geometry Seminar is at: http://www.maths.usyd.edu.au/u/SemConf/Geometry/index.html