Geometry Seminar: Milman -- Nash Desingularization for Binomial Varieties as Euclidean Multidimensional Division

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")

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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