Noticias en español
Maker-Breaker games on Galton-Watson tres.
Resumen: Maker-Breaker is a classical combinatorial game in which one player fixates, the other one removes edges (taking turns) in order to connect/isolate nodes. This two-player game is considered on the random board given by the family tree of a supercritical Galton-Watson branching proces Strategies and success probabilities are assessed for different levels of information, the players receive during play.
Read MoreThe Korteweg-de Vries on the general star graphs
Abstract: In this talk, we discuss local well-posedness for the Cauchy problem associated with the Korteweg-de Vries (KdV) equation on a general metric star graph. The graph comprises (m+k) semi-infinite edges: k negative half-lines and m positive half-lines, all joined at a common vertex. The choice of boundary conditions is compatible with the conditions determined by the semigroup theory. The crucial point in this work is to obtain the integral formula using the forcing operator method. This work extends the previous results obtained by [2018 Cavalcante] for the specific case of the...
Read MoreWell-Posedness results for non-isotropic perturbations of the nonlinear Schrödinger equation on cylindrical domains
Abstract: We consider a non-isotropically perturbed nonlinear Schrödinger equation posed on two-dimensional cylindrical domains of the form T×R T and R×T. This equation arises in models describing wave propagation in fiber arrays. In this talk, we present several well-posedness results for initial data belonging to Sobolev spaces. For the cylindrical domain T×R, we establish global well-posedness in L^2xL^2 for small initial data by proving an L^4 – L^2 Strichartz-type inequality. In the case of the domain R×T, we were unable to adapt the same estimate, so we employed a different...
Read MoreDeterministic and stochastic fixed-point iterations in normed spaces.
Abstract: In this talk, we present a survey of techniques and results on error bounds and convergence rates for both deterministic and stochastic fixed-point iterations, with a focus on methods such as the Krasnoselskii-Mann and Halpern iterations. Our primary emphasis is on general normed spaces, where we employ tools from optimal transport to derive tight error bounds. For spaces with additional structure, such as Hilbert spaces, we also discuss existing techniques and the sharp results established in the literature. Finally, we highlight applications of these findings in reinforcement...
Read MoreOn the complexity of the CSP.
Abstract: The Constraint Satisfaction Problem (CSP) is defined as follows: we are given a set of variables, a set of values, and a set of constraints, where each constraint restricts the combination of values that certain tuple of variables can take. The question is whether there exists an assignment of values to the variables that satisfies all the constraints. The CSP is a well-known NP-complete problem, and hence much research has been done to identify restrictions of this problem that can be solved in polynomial time. In this talk, we focus on the so-called structural restrictions, that...
Read MoreSome dynamical invariants under strong orbit equivalence.
Abstract: A dynamical system is usually made up of a state space and a rule (a map acting on the space) that tells us how the system evolves over time. One of the central questions in studying these systems is figuring out when two of them are essentially the same, or conjugate, as we usually say. There are several known features, called invariants, that stay the same under conjugacy, but so far, no single invariant can completely characterize when two systems are conjugate. Because of that, it is natural to look at a slightly weaker idea of equivalence, called strong orbit equivalence. All...
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