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
We consider skew product extensions over symmetric interval exchange transformations on the unit interval [0,1) with respect to the cocycle f = χ(0,½) - χ(½,1). We prove that for almost every interval exchange transformation ...
We prove that skew products with the cocycle given by the function f(x) = a(x − 1/2) with a ̸= 0 are ergodic for every ergodic symmetric IET in the base, thus giving the full characterization of ergodic extensions in ...
We produce affine interval exchange transformations (AIETs) which are topologically conjugated to (standard) interval exchange maps (IETs) via a singular conjugacy, i.e. a diffeomorphism h of [0,1] which is C0 but not C1 ...
Recently, a substantial progress in studying the problem of optimal sampling recovery was made in a number of papers. In particular, this resulted in some progress in studying sampling recovery on function classes with ...
A separating system of a graph (Formula presented.) is a family (Formula presented.) of subgraphs of (Formula presented.) for which the following holds: for all distinct edges (Formula presented.) and (Formula presented.) ...
This survey focuses on the application of Lagrangian descriptors to reveal the geometry of phase space structures that determine transport in dynamical systems. We present diverse formulations of the method and examine ...
We present an algorithm for the construction of lower dimensional elliptic tori in parametric Hamiltonian systems by means of the parametrization method with the tangent and normal frequencies being prescribed. This requires ...
A novel mathematical model is developed to describe column adsorption when the contaminant constitutes a significant amount of the fluid. This requires tracking the variation of pressure and velocity, in addition to the ...
In this note we study the behavior of the coefficients of the Taylor method when computing the numerical solution of stiff Ordinary Differential Equations. First, we derive an asymptotic formula for the growth of the ...
In 1991, Moore (Nonlinearity 4:199–230, 1991) raised a question about whether hydrodynamics is capable of performing computations. Similarly, in 2016, Tao (J Am Math Soc 29(3):601–674, 2016) asked whether a mechanical ...
We present a new non-parametric approach for estimating the total number of animals or species when we only have information on the number of animals or species that have been observed once, twice, (Formula presented.), ...
A pebble tree is an ordered tree where each node receives some colored pebbles, in such a way that each unary node receives at least one pebble, and each subtree has either one more or as many leaves as pebbles of each ...
In 2000, Darmon described a program to study the generalized Fermat equation using modularity of abelian varieties of GL 2-type over totally real fields. The original approach was based on hard open conjectures, which have ...
Building upon the pioneering work of Merle, Raphaël, Rodnianski and Szeftel [67, 68, 69], we construct exact, smooth self-similar imploding solutions to the 3D isentropic compressible Euler equations for ideal gases for ...
By considering planar slow-fast systems with a curve of double singular points, we obtain lower bounds on the number of limit cycles of polynomial systems surrounding a single singular point, as well as on the number of ...
In this article, we determine the automorphism group of all the quotient modular curves of the modular curve X0(pq), where p,q are two distinct primes. In obtaining such results, we provide different insights to compute ...
We study the local geometry of the moduli space of intermediate Jacobians of (2,2)-threefolds in P2× P2. More precisely, we prove that a composition of the second fundamental form of the Siegel metric in A9 restricted to ...
We discuss the Hölder regularity of solutions to the semilinear equation involving the fractional Laplacian (−Δ)su=f(u) in one dimension. We put in evidence a new regularity phenomenon which is a combined effect of the ...
We push forward the study of higher dimensional stable Hamiltonian topology by establishing two nondensity results. First, we prove that stable hypersurfaces are not (Formula presented.) -dense in any isotopy class of ...
We investigate the small constant case of a characterization of A∞ weights due to Fefferman, Kenig and Pipher. In their work, Fefferman, Kenig and Pipher bound the logarithm of the A∞ constant by the Carleson norm of a ...
