Geodesic
The degree one Laguerre–Pólya class and the shuffle-word-embedding conjecture
Canadian mathematical bulletin, Tome 67 (2024) no. 3, pp. 760-767

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DOI

We discuss the class of functions, which are well approximated on compacta by the geometric mean of the eigenvalues of a unital (completely) positive map into a matrix algebra or more generally a type $II_1$ factor, using the notion of a Fuglede–Kadison determinant. In two variables, the two classes are the same, but in three or more noncommuting variables, there are generally functions arising from type $II_1$ von Neumann algebras, due to the recently established failure of the Connes embedding conjecture. The question of whether or not approximability holds for scalar inputs is shown to be equivalent to a restricted form of the Connes embedding conjecture, the so-called shuffle-word-embedding conjecture.
DOI : 10.4153/S0008439524000146
Mots-clés : Radical Laguerre–Pólya class, BMV polynomials, Connes embedding conjecture, shuffle-word-embedding conjecture 
Pascoe, James E.; Woerdeman, Hugo J. The degree one Laguerre–Pólya class and the shuffle-word-embedding conjecture. Canadian mathematical bulletin, Tome 67 (2024) no. 3, pp. 760-767. doi: 10.4153/S0008439524000146
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     title = {The degree one {Laguerre{\textendash}P\'olya} class and the shuffle-word-embedding conjecture},
     journal = {Canadian mathematical bulletin},
     pages = {760--767},
     year = {2024},
     volume = {67},
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     doi = {10.4153/S0008439524000146},
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