We study the geometry of Hilbert spaces with complete Pick kernels and the geometry of sets in complex hyperbolic space, taking advantage of the correspondence between the two topics. We focus on questions of assembling Hilbert spaces into larger space…
In this article, we are concerned with the tempered fractional parabolic problem where is a tempered fractional operator with and is a sufficiently small positive constant. We first establish maximum principle principles for problems involving tempe…
We show that the total variation mixing time is not quasi-isometry invariant, even for Cayley graphs. Namely, we construct a sequence of pairs of Cayley graphs with maps between them that twist the metric in a bounded way, while the ratio of the two mi…
Inspired by a remarkable work of Félix, Halperin, and Thomas on the asymptotic estimation of the ranks of rational homotopy groups, and more recent works of Wu and the authors on local hyperbolicity, we prove two asymptotic formulae for torsion rank of…
We use the cobordism distance on the smooth knot concordance group to measure how close two knots are to being linearly dependent. Our measure, , is built by minimizing the cobordism distance between all pairs of knots, and , in cyclic subgroups cont…
Consider a minimal-free topological dynamical system . It is shown that the radius of comparison of the crossed product C*-algebra is at most half the mean topological dimension of . As a consequence, the C*-algebra is classified by the Elliott invar…
We prove quantitative bounds for the inverse theorem for Gowers uniformity norms and in . The proof starts from an earlier partial result of Gowers and the author which reduces the inverse problem to a study of algebraic properties of certain multili…
Let be a hereditary collection of finite subsets of . In this paper, we introduce and characterize -(almost) greedy bases. Given such a family , a basis for a Banach space X is called -greedy if there is a constant such that for each , , and , we ha…