The AROMATH seminar will usually happen on Tuesday at 10h30-11h30 every two weeks, except for a few deviations.
The presentations will typically take place at Inria Sophia Antipolis, Byron Blanc 106, and also online.
To join online, at https://cutt.ly/aromath or with a web browser at https://cutt.ly/aromath-web
use meeting ID: 828 5859 7791, passcode: 123
Agnes Szanto - Certification of Isolated Roots of Overdetermined and Singular Polynomial Systems, and their Multiplicity Structure
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11 April 2018
This talk is concerned with certifying that a given point is near an exact root of an overdetermined or singular polynomial system with rational coefficients. The difficulty lies in the fact that consistency of overdetermined systems is not a continuous property. Our certification is based on hybrid symbolic-numeric methods. In the first part of the talk we describe an algorithm to certify approximate roots of exact overdetermined systems over Q, and analyze its bit complexity. In the second part of the talk we certify points near exact singular roots, using new improved versions of the so called isosingular deflation method. Moreover, we also give a new algorithm that computes and certifies the multiplicity structure of the exact root near our given point. This is a joint work with Tulay Akoglu, Jonathan Hauenstein and Bernard Mourrain.
Agnes Szanto (North Carolina State University, Raleigh, USA)
