We revisit the notion of tracial approximation for unital simple -algebras. We show that a unital simple separable infinite dimensional -algebra A is asymptotically tracially in the class of -algebras with finite nuclear dimension if and only if A is a…
The peeling process, which describes a step-by-step exploration of a planar map, has been instrumental in addressing percolation problems on random infinite planar maps. Bond and face percolations on maps with faces of arbitrary degree are conveniently…
This paper studies a new Whitney type inequality on a compact domain
that takes the form
where
denotes the rth order directional modulus of smoothness of
along a finite set of directions
such that
,
. We prove that there does not exist a un…
We study harmonic analysis on the symmetric space . We prove several standard results, e.g. Shalika germ expansion of orbital integrals, representability of the Fourier transform of orbital integrals and representability of spherical characters. These …
We study webs in quantum type C, focusing on the rank three case. We define a linear pivotal category diagrammatically by generators and relations, and conjecture that it is equivalent to the category
of quantum
representations generated by the fu…
We show that in a parametric family of linear recurrence sequences with the coefficients and characteristic roots , , given by rational functions over some number field, for all but a set of elements of bounded height in the algebraic closure of , t…
We obtain sharp ranges of -boundedness for domains in a wide class of Reinhardt domains representable as sublevel sets of monomials, by expressing them as quotients of simpler domains. We prove a general transformation law relating -boundedness on a do…
For a finite-dimensional Hopf algebra
, the McKay matrix
of an
-module
encodes the relations for tensoring the simple
-modules with
. We prove results about the eigenvalues and the right and left (generalized) eigenvectors of
by relating them…
In the integral Khovanov homology of links, the presence of odd torsion is rare. Homologically thin links, that is, links whose Khovanov homology is supported on two adjacent diagonals, are known to contain only torsion. In this paper, we prove a loca…
We initiate the program of extending to higher-rank graphs (k-graphs) the geometric classification of directed graph -algebras, as completed in Eilers et al. (2016, Preprint). To be precise, we identify four “moves,” or modifications, one can perform o…