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Introduction to Grobner bases
Date: 2018/9/30             Browse: 39

Speaker:     Prof. Aldo Conca

Time:          15:00—16:30, Sept 27

Location:    Room 1A-200, SIST Building

Host:          Prof. Manolis C. Tsakiris

Abstract:

Grobner basis and related algorithms can be seen as generalizations of Gaussian elimination for linear systems and Euclid's algorithm for computing polynomial greatest common divisors of univariate polynomials.  They can be used to solve algorithmically questions related to polynomials as, for example, the following:

1) deciding whether a system of polynomial equations has solutions, 

2) deciding whether a polynomial can be written as linear combinations with polynomial coefficients of given polynomials,

3) deciding whether a polynomial can be written as polynomial function of given polynomials,

4) find the implicit equations of a locus given by a polynomial parametrization.

Questions of this type and their variations have several applications in science and engineering, such as computer vision, machine learning, data science, robotics, physics and biology.

The goal of the talk is to present a gentle introduction to Grobner bases and related algorithms and their use to answer the questions above.

Bio: 

Aldo Conca received his PhD from the University of Essen (Germany) in 1993 with a thesis written under the direction of Prof. J. Herzog.

Since 2001 he is professor at the University of Genova (Italy) and presently he is the head of his department. He has written over 70 papers devoted to commutative algebra, i.e. essentially the study of the algebraic structures related to polynomials.  He has been visiting professor at MSRI Berkeley and organizer of conferences in Oberwolfach.

SIST-Seminar 18073