Metric Functionals and Weak Convergence
We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested …
Professional Summary
I’m a Researcher in Mathematics. I’ve carried out research at Aalto University, Inria Saclay, and VTT. I’ve made contributions to metric geometry, functional analysis and optimization. I’m passionate about quantum computing, risk analysis and optimization algorithms.
Education
DSc Mathematics
Aalto University
Interests
Metric Geometry
Quantum Computing
Risk Analysis
Optimization Algorithms
Featured Publications
Subinvariant Metric Functionals for Nonexpansive Mappings
We investigate the existence of subinvariant metric functionals for commuting families of nonexpansive mappings in noncompact subsets of Banach spaces. Our findings underscore the …
Firm non-expansive mappings in weak metric spaces
We introduce the notion of firm non-expansive mapping in weak metric spaces, extending previous work for Banach spaces and certain geodesic spaces. We prove that, for firm …
Comments on the cosmic convergence of nonexpansive maps
This note discusses some aspects of the asymptotic behaviour of nonexpansive maps. Using metric functionals, we make a connection to the invariant subspace problem and prove a new …
Characterizing the metric compactification of \(L_p\) spaces by random measures
We present a complete characterization of the metric compactification of \(L_p\) spaces for \(1\leq p < \infty\). Each element of the metric compactification of \(L_p\) is …
On the Metric Compactification of Infinite Dimensional \(\ell_p\) Spaces
The notion of metric compactification was introduced by Gromov and later rediscovered by Rieffel. It has been mainly studied on proper geodesic metric spaces. We present here a …
The Horofunction Boundary of Finite Dimensional \(\ell_p\) Spaces
We give a complete description of the horofunction boundary of finite dimensional \(\ell_p\) spaces for \(1\leq p \leq \infty\). We also study the variation norm on …