报告题目：1\he Hilbert-Hankel Problem

报告人：   祁力群 教授 （香港理工大学应用数学系） 时  间：   2014年12月26日14:00 - 15:00

地点：数学与计算机科学学院6号楼309报告厅

  摘  要：It was shown by young Hilbert in 1888 that for homogeneous polynomial, only in the following three cases, a PSD polynomial definitely is an SOS polynomial: 1) n = 2; 2) m = 2; 3) m=4 and n=3. For tensors, the second case corresponds to the symmetric matrices, i.e., a PSD symmetric matrix is always an SOS matrix.   Hilbert proved that in all the other possible combinations of m=2k and n, there are non-SOS PSD homogeneous polynomials.

Recently, we raised a question, is a PSD Hankel tensor always an SOS tensor? If the answer to this question is ``yes'', then the problem for determining a given even order Hankel tensor is PSD or not is polynomial time solvable. Hence, this problem has important practical significance.   On the other hand, theoretically, this is a Hilbert problem under the Hankel constraint.  We discussed with the experts of the Hilbert problem: Bruce Reznick and Man-Duen Choi. The Hilbert-Hankel problem is a new open problem It is challenging. It has strong theoretical and important practical significance. I hope that some of you may be attracted to explore this problem