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What and Who
Title:A τ-conjecture for Newton polygons.
Speaker:Pascal Koiran
coming from:ENS Lyon
Speakers Bio:
Event Type:Talk
Visibility:D1, D2, D3, D4, D5, SWS, RG1, MMCI
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Level:Expert Audience
Date, Time and Location
Date:Thursday, 27 March 2014
Duration:60 Minutes
Building:E2 1 - Bioinformatik
One can associate to any bivariate polynomial P(X,Y) its Newton polygon. This is the convex hull of the points (i,j) such that the monomial XiYj appears in P with a nonzero coefficient. We conjecture that when P is expressed as a sum of products of sparse polynomials, the number of edges of its Newton polygon is polynomially bounded in the size of such an expression. We show that this ``τ-conjecture for Newton polygons,'' even in a weak form, implies that the permanent polynomial is not computable by polynomial size arithmetic circuits. We make the same observation for a weak version of an earlier ``real τ-conjecture.'' Finally, we make some progress toward the τ-conjecture for Newton polygons using recent results from combinatorial geometry.

This talk is based on joint work with Natacha Portier, Sébastien Tavenas and Stéphan Thomassé. I will present our results and conjectures, starting from the very basic properties of Newton polygons (and in particular the role of Minkowski sum).

Name(s):Markus Bläser
EMail:--email address not disclosed on the web
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  • Christine Kiesel, 03/19/2014 04:45 PM
  • Christine Kiesel, 03/19/2014 04:36 PM -- Created document.