Noticias en español
Stochastic models with age structure under harvesting: existence, approximation and estimation.
Resumen: In this talk, we will present the development and analysis of a mathematical model for the kelp population, which integrates ecological and sociological aspects, in particular the response of harvesters to environmental regulations through parametrised decision rules. We will begin with a heuristic derivation of the model, incorporating the uncertainty inherent in open systems. We will then address the theoretical analysis, establishing conditions for the existence and uniqueness of admissible solutions in our context, the characterisation of asymptotic extinction scenarios and...
Read MoreImproveApproximation Algorithms for Path and Forest Augmentation via a Novel Relaxation
Abstract: The Forest Augmentation Problem (FAP) asks for a minimum set of additional edges (links) that make a given forest 2-edge-connected while spanning all vertices. A key special case is the Path Augmentation Problem (PAP), where the input forest consists of vertex-disjoint paths. Grandoni, Jabal Ameli, and Traub [STOC’22] recently broke the long-standing 2-approximation barrier for FAP, achieving a 1.9973-approximation. A crucial component of this result was their 1.9913-approximation for PAP; the first better-than-2 approximation for PAP. In this work, we improve these results...
Read MoreInverse scattering for asymptotically hyperbolic manifolds.
RESUMEN: On compact Riemannian manifolds with boundary, the (anisotropic) Calderón’s problem asks to what extent the Dirichlet-to-Neumann map associated with the Laplace—Beltrami equation determines the metric (up to a natural obstruction). In this talk, I will discuss a similar problem, known as inverse scattering for asymptotically hyperbolic manifolds (i.e., manifolds that, outside a compact region, behave like the hyperbolic space): fixed an “energy level”, and given the analog of the Neumann data for solutions to certain 0-elliptic PDE depending on the fixed energy...
Read MoreLinearized marked length spectrum rigidity for general Anosov flows.
RESUMEN: In this talk I will present some work in progress in a linearized version of the marked length spectrum rigidity for general Anosov flows (also known as Burns-Katok conjecture). I will begin with an introduction to the microlocal techniques used by Guillarmou and Lefeuvre to solve the problem in the case where metrics of negative curvature are close enough. Then, I will show how to generalize some aspects from the geodesic flow to more general ones, as the magnetic or thermostat flows, under some reasonable dynamical assumptions.
Read MoreRenormalized Volume/Area from Conformal Gravity
Abstract: We introduce a mechanism (Conformal Renormalization) to cancel divergences in Einstein gravity for asymptotically hyperbolic Einstein (AHE) spaces. In the bulk, the procedure amounts to embedding Einstein gravity in Conformal Gravity, whose action is given by a conformal invariant in four dimensions. This scheme is proved to be equivalent to both holographic techniques (for physicists) and the notion of Renormalized Volume (for mathematicians). In turn, for surfaces anchored to the conformal boundary of AHE spaces, its area and other co-dimension 2 functionals also exhibit a...
Read MoreAnalyticity of The Lyapunov Exponents of Random Products of Matrices.
RESUMEN: In this talk, we extend the results and methods of Y. Peres from a finite to an infinite (but compact) space of symbols. In other words, we establish the analyticity of the maximal Lyapunov exponent for independent and identically random products of matrices as a function of the transition probabilities. Our approach combines the spectral properties of the associated Markov operator with the theory of holomorphic functions in Banach spaces. This is a joint work with Artur Amorim and Marcelo Durães.
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