Mathematics Colloquium.
Speaker: Marie-Francoise Roy.
Affiliation: University of Rennes.
Date and Time: Monday 10 February, 04:00 pm - 05:00 pm.
Venue: Room 216, Department of Mathematics.
Title: Hilbert 17th problem: classical proof and recent effectivity results.
Abstract: Hilbert 17th problem is asking whether a non negative polynomial
is always a sum of squares. We discuss Artin’s (1927) positive answer to
this problem and explain why this answer did not provide an effective
method for constructing the sum of squares. We describe primitive
recursive effective results obtained by Kreisel and his students in the
fifties. Finally we explain the first elementary recursive degree bound we
obtain, a tower of five exponentials. A precise bound in terms of the
number and degree of the polynomials and their number of variables is
provided. This is a joint work with Henri Lombardi and Daniel Perrucci.
5:00pm
6:00pm
Time:
4:00pm-5:00pm
Location:
Room No 216 Department of Mathematics
Description:
Mathematics Colloquium.
Speaker: Marie-Francoise Roy.
Affiliation: University of Rennes.
Date and Time: Monday 10 February, 04:00 pm - 05:00 pm.
Venue: Room 216, Department of Mathematics.
Title: Hilbert 17th problem: classical proof and recent effectivity results.
Abstract: Hilbert 17th problem is asking whether a non negative polynomial
is always a sum of squares. We discuss Artin’s (1927) positive answer to
this problem and explain why this answer did not provide an effective
method for constructing the sum of squares. We describe primitive
recursive effective results obtained by Kreisel and his students in the
fifties. Finally we explain the first elementary recursive degree bound we
obtain, a tower of five exponentials. A precise bound in terms of the
number and degree of the polynomials and their number of variables is
provided. This is a joint work with Henri Lombardi and Daniel Perrucci.