Abstract for the talk on 11.04.2019 (11:00 h)Special Lecture
Dmitrii Pasechnik (University of Oxford)
An efficient sum of squares certificate for 4-ary 4-ic
We show that for any non-negative quaternary quartic form f there exists a product of two non-negative quadrics q so that qf is a sum of squares (s.o.s.) of quartics. This is a much better upper bound on the degree of a multiplier needed to demonstrate nonnegativity of f via an s.o.s. decomposition than known previously; similar almost tight bounds are only known for ternary forms. As a step towards deciding whether it is suﬃcient to use a quadratic multiplier q, we show that there exist non-s.o.s. non negative ternary sextics ac − b2, with a, b, c of degrees 2, 3, 4, respectively.