6 papers
Extreme points and faces in the moment problem
Didier Henrion, Martin KružÃk, Stephan Weis
The polyconvex envelope, used in the calculus of variations and elasticity theory, was expressed by Dacorogna pointwise as a linear program on finitely atomic measures on the space…
The joint numerical range of three hermitian matrices
Piotr Pikul, Ilya Spitkovsky, Konrad SzymaÅski +2
We analyze the joint numerical range of three hermitian matrices of order four. In the generic case, this three-dimensional convex set has a smooth boundary. We analyze non-gen…
Polyconvexity with Moments and Sums of Squares
Giovanni Fantuzzi, Didier Henrion, Martin Kru{ž}Ãk +2
A function of a matrix is polyconvex when it can be expressed as a convex function of the matrix minors. Polyconvexity is a regularity condition ensuring existence of minimizers in…
Protocols for Quantum Weak Coin Flipping
Atul Singh Arora, Jérémie Roland, Chrysoula Vlachou +1
Weak coin flipping is an important cryptographic primitive$\unicode{x2013}$it is the strongest known secure two-party computation primitive that classically becomes secure only und…
Matrix systems, algebras, and open maps
Stephan Weis
Every state on the algebra of complex nxn matrices restricts to a state on any matrix system. Whereas the restriction to a matrix system is generally not open, we prove that…
A note on faces of convex sets
Stephan Weis
The faces of a convex set owe their relevance to an interplay between convexity and topology that is systematically studied in the work of Rockafellar. Infinite-dimensional convex…