Comentarios:
SPEAKER: José Más, Universidad Politécnica de Valencia (https://personales.upv.es/jmasm/indexc.html) HOUR: 16:30h TITLE: H-matrices, old and new SHORT ABSTRACT: We review some results on H-matrices, from old ones to newest. -------------------------------------------------------------------------------------------------------------------------------------------- SPEAKER: Aida Abiad, Eindhoven University of Technology (https://aidaabiad.win.tue.nl/) HOUR: 17:00h TITLE: Spectral approach to Kemeny’s constant ABSTRACT: Kemeny’s constant, a fundamental parameter in the theory of Markov chains, has recently received significant attention within the graph theory community. Originally defined for a discrete, finite, time-homogeneous, and irreducible Markov chain based on its stationary vector and mean first passage times, Kemeny’s constant finds special relevance in the study of random walks on graphs. Kemeny’s constant gives a measure of how quickly a random walker can move around a graph and is thus a good measure of the connectivity of a graph. Several approximations and bounds for Kemeny’s constant have been studied in the literature. In this work, we present several new approximations and bounds for Kemeny’s constant, which we derive using spectral techniques. -------------------------------------------------------------------------------------------------------------------------------------------- SPEAKER: Ignacio Echave-Sustaeta (https://research.tue.nl/en/persons/ignacio-echave-sustaeta-rodr%C3%ADguez) TITLE: Graphical models for extremes and Laplacian matrices HOUR: 17:30h ABSTRACT: Graphical models for extremes are a way of exploring the dependence structure in the extreme setting. A particularly interesting parametric model to study is the Hüsler–Reiss distribution. We explore ways to characterize and better understand their theoretical properties. These models can be parametrized using a (signed) Laplacian matrix, and we use this fact to analyze them also from a more algebraic perspective. We find that Cayley--Menger matrices and resistance-based invariants allow for a simplified density representation and algebraic description of conditional independence in these models. Finally, we comment on our current ideas for future work within this project. This is joint work with Frank Röttger. -------------------------------------------------------------------------------------------------------------------------------------------- SPEAKER: Alicia Roca, Universidad Politécnica de Valencia (https://www.upv.es/ficha-personal/aroca) TITLE: Isomorphisms between lattices of hyperinvariant subspaces HOUR: 18:00h ABSTRACT: Given two nilpotent endomorphisms on complex vector spaces, we determine when their lattices of hyperinvariant subspaces are isomorphic. The study of the lattice of hyperinvariant subspaces can be reduced to the nilpotent case when the endomorphism has a Jordan-Chevalley decomposition; in particular, it occurs if the underlying field is the field of complex numbers. This is joint work with David Mingueza (Nestle España) y Eulalia Montoro (Universidad de Barcelona).