Thursday, October 15, 2026 - 16:00 in V2-210/216
A Geometric Study of Nonnegative and Psd Rank: Hard Problems, Solvable Small Cases
A talk in the Mathematisches Kolloquium series by
Kaie Kubjas from Aalto University
| Abstract: |
Nonnegative rank and positive semidefinite (psd) rank are two notions of conic rank that generalize the usual matrix rank by requiring the factors to lie in the nonnegative orthant or the psd cone, respectively. These factorizations arise naturally in optimization, statistics, and quantum information. Both ranks are known to be computationally hard to compute in general, which makes complete answers rare.
In this talk I will describe a body of work aimed at understanding these ranks in the smallest cases where complete answers are possible: nonnegative rank 3 and psd rank 2. There, I'll present results on semialgebraic descriptions, their boundaries, and uniqueness of factorizations. In addition to the specific results, I will try to convey the broader geometric intuition they offer for the general setting.
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