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Exploiting term sparsity in noncommutative polynomial optimization
We provide a new hierarchy of semidefinite programming relaxations, called NCTSSOS , to solve large-scale sparse noncommutative polynomial...
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Noncommutative Geometry of Random Surfaces
AbstractWe associate a noncommutative curve to a periodic, bipartite, planar dimer model with polygonal boundary. It determines the inverse...
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On Noncommutative Vieta Theorem in Geometric Algebras
In this paper, we discuss a generalization of Vieta theorem (Vieta’s formulas) to the case of Clifford geometric algebras. We compare the generalized...
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Nonlinear partial differential equations on noncommutative Euclidean spaces
Noncommutative Euclidean spaces—otherwise known as Moyal spaces or quantum Euclidean spaces—are a standard example of a non-compact noncommutative...
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Convergence for noncommutative rational functions evaluated in random matrices
One of the main applications of free probability is to show that for appropriately chosen independent copies of d random matrix models, any...
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Operator Theory on Noncommutative Polydomains, I
The goal of this paper is to study the noncommutative polydomains and their universal operator models generated by admissible k-tuples of formal...
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Globally trace-positive noncommutative polynomials and the unbounded tracial moment problem
A noncommutative (nc ) polynomial is called (globally) trace-positive if its evaluation at any tuple of operators in a tracial von Neumann algebra...
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Picard schemes of noncommutative bielliptic surfaces
We study the nontrivial elements in the Brauer group of a bielliptic surface and show that they can be realized as Azumaya algebras with a simple...
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Noncommutative Gröbner Bases and Ext Groups
We consider a theory of noncommutative Gröbner bases on decreasingly filtered algebras whose associated graded algebras are commutative. We transfer...
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Sparse noncommutative polynomial optimization
This article focuses on optimization of polynomials in noncommuting variables, while taking into account sparsity in the input data. A converging...
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L-functions of noncommutative tori
We introduce an analog of the L -function for noncommutative tori. It is proved that such a function coincides with the Hasse–Weil L -function of an...
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The Emergence of Noncommutative Potential Theory
We review origins and developments of Noncommutative Potential Theory as underpinned by the notion of energy form. Recent and new applications are...
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A Brief Introduction to Noncommutative Function Theory
This survey provides a very brief introduction to the notion of a noncommutative function, with a particular emphasis on those parts of the theory...
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Growth of generalized Weyl algebras over polynomial algebras and Laurent polynomial algebras
We study the growth and Gelfand-Kirillov dimension (GK-dimension) of the generalized Weyl algebra (GWA) A = D ( σ, a ), where D is a polynomial algebra...
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Commuting row contractions with polynomial characteristic functions
A characteristic function is a special operator-valued analytic function defined on the open unit ball of ℂ n associated with an n-tuple of commuting...
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Noncommutative Catalan Numbers
The goal of this paper is to introduce and study noncommutative Catalan numbers Cn which belong to the free Laurent polynomial algebra Ln in n...
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Weighted Hardy Spaces Over the Unit Ball: The Freely Noncommutative and Commutative Settings
It is known that backward-shift-invariant subspaces of the Hardy space...
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Sheaves of Noncommutative Smooth and Holomorphic Functions Associated with the Non-Abelian Two-Dimensional Lie Algebra
AbstractDosi and, quite recently, the author showed that, on the character space of a nilpotent Lie algebra, there exists a sheaf of...