Combinatorics and Optimization Mathematics PhD student Stefan Sremac was one of six students who won the 2019 Huawei Prize for Best Research Paper by a Mathematics Graduate Student. This award recognizes the impact of his paper, Maximum determinant positive definite Toeplitz completions, with a prize of $4,000.
Sremac’s research focused on matrix completion problems. Along with his supervisor Henry Wolkowicz and collaborator Hugo Woerdeman, he characterized the patterns of of a partial Toeplitz matrix for which the maximum determinant positive definite completion is Toeplitz.
This problem may be categorized broadly as an instance of ‘matrix completion’, a more general problem that has received a lot of attention throughout the years. Literature on Toeplitz positive definite completions dates back to the 1980s in work by Dym and Gohberg. Fast forward to 2005, He and Ng suggested that if a partial matrix with the generalized cycle pattern admits a positive definite completion, then it admits a Toeplitz positive definite completion. As a result of Sremac’s paper, we now know that this conjecture is true.
“Aside from the main results, a contribution of this paper is the marriage of this specific type of matrix completion problem with deep results from semidefinite optimization that may not be known to many researchers,” said Wolkowicz. “Our result provides a blueprint for analyzing other classes of problems such as positive definite Hankel completions or those involving the displacement matrices, among which are Cauchy and Vandermonde matrices.”
The research was accepted for publication to the Operator Theory, Analysis and the State Space Approach that was produced to celebrate the contributions of Rien Kaashoek on his 80th birthday.
The 2019 Huawei Prize for Best Research Paper by a Mathematics Graduate Student would not be possible without the generous support from Huawei.