Let \mathcal{L}(X,Y) denote the normed vector space of all continuous operators from \(X\) to \(Y\), \(X^*\) be the dual space of \(X\), and \(\mathcal{K}(X,Y)\) denote the collection of all compact […]
Quantum metrics in the sense of Rieffel were introduced to prove some statements arising in the high-energy physics literature. Since then, the area of quantum metric geometry has been used […]
We introduce a family of norms on the space of self-adjoint trace class symmetric tensor power of linear operators acting on an infinite-dimensional Hilbert space. Our technique is to extend to infinite dimension an original and nice idea of a very recent result by K. Aguilar, Á. Chávez, S. R. Garcia and J. Volčič, in […]
Let x_1,...,x_n be an overdetermined spanning set for the Euclidean space R^k, where n > k. Let L be the integer span of these vectors. Then L is an additive subgroup of R^n. When is it discrete in R^n? Naturally, this depends on the choice of the spanning set, but in which way? We will […]
We introduce the notion of linear multifractional stable sheets in the broad sense (LMSS) to include both linear multifractional Brownian sheets and linear multifractional stable sheets. The purpose of the […]
Graph products of groups were introduced in E. Green’s thesis in the 90’s as generalizations of Right-Angled Artin Groups. These have become objects of intense study due to their key […]
Given a unital AF (approximately finite-dimensional) algebra A equipped with a faithful tracial state, we equip each (norm-closed two-sided) ideal of A with a metrized quantum vector bundle structure, when […]
We comment on the main steps to take when studying some variational problems. This includes optimization problems arising in geometry, machine learning, non linear elasticity, fluid mechanics, etc... For the […]
In this talk we discuss the Hilbert space approach, or the variational approach, in the study of questions of existence and multiplicity for some two-point boundary-value problems for nonlinear, second […]
Using elementary methods from differential equations and analysis we will consider the existence and multiplicity of solutions to semilinear partial differential equations with boundary conditions.
The Effros-Shen algebra corresponding to an irrational number $\theta$ can be described by an inductive sequence of direct sums of matrix algebras, where the continued fraction expansion of $\theta$ encodes the dimensions of the summands, and how the matrix algebras at the nth level fit into the summands at the (n+1)th level. In recent work, […]
Title: Developments in Noncommutative Fractal Geometry Abstract: As a noncommutative fractal geometer, I look for new expressions of the geometry of a fractal through the lens of noncommutative geometry. At the quantum scale, the wave function of a particle, but not its path in space, can be studied. Riemannian methods often rely on smooth paths to encode […]
