116 citations · 1.1k across the 72 of their papers we have counts for
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Matrix Convex Hulls of Free Semialgebraic Sets
J. William Helton, Igor Klep, Scott McCullough
This article resides in the realm of the noncommutative (free) analog of real algebraic geometry - the study of polynomial inequalities and equations over the real numbers - with a…
Noncommutative polynomials nonnegative on a variety intersect a convex set
J. William Helton, Igor Klep, Christopher S. Nelson
By a result of Helton and McCullough, open bounded convex free semialgebraic sets are exactly open (matricial) solution sets D_L of a linear matrix inequality (LMI) L(X)>0. This pa…
Free Convex Algebraic Geometry
J. William Helton, Igor Klep, Scott McCullough
This chapter is a tutorial on techniques and results in free convex algebraic geometry and free real algebraic geometry (RAG). The term free refers to the central role played by al…
Correction of a proof in "Connes' embedding conjecture and sums of hermitian squares"
Sabine Burgdorf, Ken Dykema, Igor Klep +1
We show that Connes' embedding conjecture (CEC) is equivalent to a real version of the same (RCEC). Moreover, we show that RCEC is equivalent to a real, purely algebraic statement…