SMS scnews item created by Zhou Zhang at Fri 11 May 2012 1023
Type: Seminar
Distribution: World
Expiry: 1 Jun 2012
Calendar1: 15 May 2012 1200-1300
CalLoc1: Carslaw 352
Auth: zhangou@bari.maths.usyd.edu.au

# Geometry Seminar: Milman -- Nash Desingularization for Binomial Varieties as Euclidean Multidimensional Division, Part II

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.

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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")

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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.

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Web site for Geometry Seminar is at:

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


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