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 openscience@crm.cat
We prove that if an orientable 3-manifold M admits a complete Riemannian mètric whose scalar curvature is positive and has a subquadratic decay at infinity, then it decomposes as a (possibly infinite) connected sum of ...
We prove that skew products with the co cycle given by the function f (x) = a(x-1/2) with a not equal 0 are ergodic for every ergodic symmetric IET in the base, thus giving the full characterization of ergodic extensions ...
In this work we study the moduli spaces of instanton bundles on the flag twistor space F := F (0, 1, 2). We stratify them in terms of the minimal twist supporting global sections and we introduce the notion of (special) ...
In McGehee (J Differ Equ 14:70–88, 1973) McGehee introduced a compactification of the phase space of the restricted 3-body problem by gluing a manifold of periodic orbits “at infinity”. Although from the dynamical point ...
Let R be a domain of Krull dimension one. We study when the class F of modules over R that are arbitrary direct sums of finitely generated torsion-free modules is closed under direct summands. If R is local, we show that ...
We prove that solutions to the Boltzmann equation without cut-off satisfying pointwise bounds on some observables (mass, pressure, and suitable moments) enjoy a uniform bound in L∞ in the case of hard potentials. As a ...
We prove that for every gamma>0 there exists n(0)is an element of N such that for every n >= n(0) any family of up to n(1/2-gamma) trees having at most (1-gamma)n vertices in each bipartition class can be packed into ...
Using a dataset of stars from a barred galaxy that provides instantaneous positions and velocities in the sky, we propose a method to identify its key structures, such as the central bar and spiral arms, and to determine ...
We describe an efficient iterative algorithm for the computation of theta functions of non-archimedean Schottky groups and, more generally, of (non-archimedean) discontinuous groups.
In the last decade, some algebraic tools have been successfully applied to phylogenetic reconstruction. These tools are mainly based on the knowledge of equations describing algebraic varieties associated to Markov processes ...
Memory systems with biologically constrained synapses have been the topic of intense theoretical study for over thirty years. Perhaps the most fundamental and far-reaching finding from this work is that the storage of new ...
We consider smooth families of planar polynomial vector fields {X mu}mu is an element of Lambda, where Lambda is an open subset of RN, for which there is a hyperbolic polycycle Gamma that is persistent (i.e., such that ...
This work addresses Faber-Krahn-type inequalities for quantum dot Dirac operators with nonnegative mass on bounded domains in R2. We show that this family of inequalities is equivalent to a family of Faber-Krahn-type ...
Exponential small splitting of separatrices in the singular perturbation theory leads generally to nonvanishing oscillations near a saddle-center point and to nonexistence of a true homoclinic orbit. It was conjectured ...
We study the family of operators {ℛ_a}_(a∈[0,+∞))associated to the Robin-type problems in a bounded domain Ω⊂R^2 {︄−Δu=f in Ω, 2ν¯∂_(z¯)u+au=0 on ∂Ω, and their dependency on the boundary parameter a as it moves along ...
In this paper we characterise the energy minimisers of a class of nonlocal interaction energies where the attraction is quadratic, and the repulsion is Riesz-like and anisotropic. In particular we show that, if the Fourier ...
We prove that an inner function has finite L(p)-entropy if and only if its accumulated Mobius distortion is in L-p, 0 < p < infinity. We also study the support of the positive singular measures such that their corresponding ...
Let f : C -> C be a transcendental entire map from the Eremenko-Lyubich class B, and let zeta be an attracting periodic point of period p. We prove that the boundaries of components of the attracting basin of (the orbit ...
We study an analogue of the Ramsey multiplicity problem for additive structures, in particular establishing the minimum number of monochromatic 3-APs in 3-colorings of F3n as well as obtaining the first non-trivial lower ...
We obtain Marcinkiewicz-Zygmund (MZ) inequalities in various Banach and quasi-Banach spaces under minimal structural assumptions. Our main results show that the Bernstein inequality in a general quasi-Banach function lattice ...
