Type: Seminar

Modified: Tue 8 May 2012 1041; Tue 8 May 2012 1043

Distribution: World

Expiry: 25 May 2012

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

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 8, 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