Related papers: A Survey on Connes' Embedding Conjecture
There is a fascinating interplay and overlap between recursion theory and descriptive set theory. A particularly beautiful source of such interaction has been Martin's conjecture on Turing invariant functions. This longstanding open problem…
The operator nabla, introduced by Garsia and the author, plays a crucial role in many aspect of the study of diagonal harmonics. Besides giving several new formulas involving this operator, we show how one is lead to representation…
Sorting is one of the most used and well investigated algorithmic problem [1]. Traditional postulation supposes the sorting data archived, and the elementary operation as comparisons of two numbers. In a view of appearance of new processors…
C. Bonnaf{\'e}, M. Geck, L. Iancu, and T. Lam have conjectured a description of one-sided cells in unequal parameter Hecke algebras of type $B$ which is based on domino tableaux of arbitrary rank. In the integer case, this generalizes the…
A conjecture regarding the structure of expander graphs is discussed.
We use representations of operator systems as quotients to deduce various characterisations of the weak expectation property (WEP) for C?*-algebras. By Kirchberg's work on WEP, these results give new formulations of Connes' embedding…
The Kirchberg Embedding Problem (KEP) asks if every C*-algebra embeds into an ultrapower of the Cuntz algebra $\mathcal{O}_2$. In an effort to provide a negative solution to the KEP and motivated by the recent refutation of the Connes…
In this paper, mirror extensions of vertex operator algebras is considered via tensor categories. The mirror extension conjecture is proved.
In this paper we introduce the notion of existentially closed Leibniz algebras. Then we use HNN-extensions of Leibniz algebras in order to prove an embedding theorem.
This paper presents a groundbreaking advancement in the theory of operators defined on octonionic Hilbert spaces, successfully resolving a fundamental challenge that has persisted for over six decades. Due to the intrinsic non-associative…
Paul Halmos' work in dilation theory began with a question and its answer: Which operators on a Hilbert space can be extended to normal operators on a larger Hilbert space? The answer is interesting and subtle. The idea of representing…
We consider relationships between cubic algebras and implication algebras. We first exhibit a functorial construction of a cubic algebra from an implication algebra. Then we consider an collapse of a cubic algebra to an implication algebra…
The nonlinear geometry of operator spaces has recently started to be investigated. Many notions of nonlinear embeddability have been introduced so far, but, as noticed before by other authors, it was not clear whether they could be…
In this note, we present a conjecture on intersections of set families, and a rephrasing of the conjecture in terms of principal downsets of Boolean lattices. The conjecture informally states that, whenever we can express the measure of a…
W. M. Hirsch formulated a beautiful conjecture on diameters of convex polyhedra.I suggest a new viewpoint with the deformation and moduli of polytopes.
Determining the relationship between quantum correlation sets is a long-standing open problem. The most well-studied part of the hierarchy is captured by the chain of inclusions $\mathcal C_q \subseteq \mathcal C_{qs} \subsetneq \mathcal…
Let A be a simple, unital, exact, and finite C*-algebra which absorbs the Jiang-Su algebra Z tensorially. We prove that the Cuntz semigroup of A admits a complete order embedding into an ordered semigroup obtained from the Elliott invariant…
In this paper we survey our recent work on C*-correspondences and their associated operator algebras; in particular, on adding tails, the Shift Equivalence Problem and Hilbert bimodules.
We establish a spectral characterization theorem for the operators on complex Hilbert spaces of arbitrary dimensions that attain their norm on every closed subspace. The class of these operators is not closed under addition. Nevertheless,…
The coarse geometric Novikov conjecture provides an algorithm to determine when the higher index of an elliptic operator on a noncompact space is nonzero. The purpose of this paper is to prove the coarse geometric Novikov conjecture for…