Centres de Recerca de Catalunya (CERCA)
El CRM (www.crm.cat) és un centre de recerca independent, pertanyent a la xarxa CERCA des de l'any 2008. El centre té la doble missió de promoure tant la formació avançada com la recerca en totes les àrees de les matemàtiques, en col·laboració amb universitats i altres institucions de recerca de Catalunya. La missió del CRM inclou la transferència del coneixement basat en la recerca del centre i centrada en l'impacte social. La recerca del CRM cobreix un ventall ampli de camps, des de les matemàtiques fonamentals (àlgebra/teoria dels nombres/geometria/topologia, anàlisi i PDE, combinatòria o sistemes dinàmics) fins a les aplicades (a la biomedicina, mitigació i adaptació al canvi climàtic o riscos naturals).Està acreditada com a Unitat d'Excel·lència Maria de Maeztu pel Ministeri d'Economia i Competitivitat espanyol (convocatòria 2020) i compta amb el guardó HRS4R (Estratègia de Recursos Humans per a la Investigació; atorgada per la Comissió Europea) des del 2016. El CRM acull aproximadament a 80 investigadors sèniors i investigadors adscrits dels departaments de Matemàtiques de la UPC, UB i UAB. Cinc d'ells són becats ERC. Pel que fa a la formació i a l'intercanvi de coneixement, el CRM organitza 3-4 programes intensius de recerca cada any, que acullen uns 400 investigadors visitants anuals de mitjana, connectant la comunitat matemàtica catalana amb professionals de primer nivell (amb un 70% dels participants internacionals).
Si sou autor/a d’algun document elaborat en l’àmbit del Centre de Recerca Matemàtica i voleu publicar-lo a RECERCAT, contacteu amb crmpublicacions@crm.cat
Recently J. Mateu, J. Orobitg, and J. Verdera showed that a Hölder continuous complex dilatation supported on smooth domains is a sufficient condition for the resulting quasiconformal map to be bi-Lipschitz. Their proof ...
In the present work, we proved a refined direct theorem and an exact inverse theorem of trigonometric approximation in Orlicz spaces with weights satisfying some Muckenhoupt’s \(A_{p}\) condition. As a consequence, refined ...
We introduce the notion of \(\pi\)-cosupport as a new tool for the stable module category of a finite group scheme. In the case of a finite group, we use this to give a new proof of the classification of tensor ideal ...
We prove sharp Pitt’s inequality for the Dunkl transform in \(L^{2}(\mathbb{R}^{d}\) with the corresponding weights. As an application, we obtain the logarithmic uncertainty principle for the Dunkl transform.
A Poisson manifold \((M^{2n}, \pi)\) is \(b\)-symplectic if \(\bigwedge^{n}\pi\) is transverse to the zero section. In this paper we apply techniques of Symplectic Topology to address global questions pertaining to ...
Extreme events can come either from point processes, when the size or energy of the events is above a certain threshold, or from time series, when the intensity of a signal surpasses a threshold value. We are particularly ...
For a convex domain \(D\) bounded by the hypersurface \(\partial D\) in a space of constant curvature we give sharp bounds on the width \(R − r\) of a spherical shell with radii \(R\) and \(r\) that can enclose \(\partial ...
Sepsis is a common clinical syndrome at the intensive care unit (ICU). This condition may lead to severe sepsis, or to a more severe state of septic shock and multiorganic failure, which entails a substantial risk of death. ...
We consider a stochastically perturbed Nowak-May model of virus dynamics within a host. Using the direct Lyapunov method, we found sufficient conditions for the stability in probability of equilibrium states of this model.
The purpose of this paper is to study stable representations of partially ordered sets (posets) and compare it to the well known theory for quivers. In particular, we prove that every indecomposable representation of a ...
In this paper we analyse the melting of a spherically symmetric nanoparticle, using a continuum model which is valid down to a few nanometres. Melting point depression is accounted for by a generalised Gibbs-Thomson relation. ...
Let \(G\) be a simple Lie group of real rank one, and \(S_{\infty}^{q}\) the ideal boundary of the corresponding hyperbolic symmetric space of noncompact type (\(H_{\mathbb{R}}^{n}\), \(H_{\mathbb{C}}^{n}\) , \(H_{\mathb ...
Let \(M^{n}\), \(n \geq 5\) be a complete noncompact sub-manifold immersed in \(\mathbb{H}^{n+p}\). We will prove that there exist certain positive constants \(\alpha\), \(C\) such that if \(||H|| \leq \alpha\) and the ...
Let \(\mu = e^{-V} dx\) be a probability measure and \(T = \nabla \Phi\) be the optimal transportation mapping pushing forward \(\mu\) onto a log-concave compactly supported measure \(\nu = e^{−W} dx\). In this paper, we ...
We obtain a characterization of modulus of smoothnes of fractional order in the Lebesgue spaces \(L_{\omega}^{p}\), \(1 < p < \infty\), with weights \(\omega\) satisfying the Muckenhoupt’s \(A_{p}\) condition. Also, a ...
We present a novel method for pricing European options based on the wavelet approximation (WA) method and the characteristic function. We focus on the discounted expected payoff pricing formula, and compute it by means of ...
Despite being a paradigm of quantitative linguistics, Zipf\'\''s law for words suffers from three main problems: its formulation is ambiguous, its validity has not been tested rigorously from a statistical point of view, ...
