'This project continues and advances the research lines of my past scientific activity, in the context of a reintegration to my home scientific community and the starting of a stable academic activity with a tenure track and a subsequent permanent position.
The scientific part of the proposal is the investigation of the geometry of actions of Lie groups in several dynamical and geometrical contexts, with emphasis in their singularities, and is articulated in the following two sections:
A. Reduction Theory. Following previous research by me and other groups, I will study the reduction theory for Dirac and generalized complex geometry from both the global and local point of view. This study is a natural continuation of previous research efforts about the reduction theory of symplectic and Poisson manifolds. The main novelty is that we will focus on reduction in the case when the group action presents singularities (fixed points) in Dirac and generalized complex geometry, which is a topic yet to be explored.
B. The theory of Hamiltonian relative equilibria. In this section I intend to perform a complete reorganization of the theory of Hamiltonian relative equilibria, as well as to advance it. We will competely redesign the existing theory in a way specifically adapted to the various distinguishing features of symmetric Hamiltonian systems This is a big project started during my previous stage at the University of Manchester. We have substantially advanced this problem during that period, and we expect to have results with significant impact within the duration of this Reintegration Grant.'
'Landslides constitute a major threat in mountainous areas. In recent years the risk assessment for landslides has shifted from qualitative to quantitative. The components of the risk are the hazard and the vulnerability of the exposed elements. Although for the quantification of the hazard there is considerable ongoing research, the work for the structural and societal vulnerability is limited and the evaluations are mostly judgmental or empirical, resulting in high subjectivity.
The objective of this proposal is the development of analytical methodologies to be applied for the quantification of the vulnerability of buildings and people that are threatened by rockfalls and slides. Two load-bearing systems will be considered: reinforced-concrete, RC, and masonry structures. Additionally, the societal vulnerability will be calculated based on the potential extent of the building damage. The methodologies will be applied to selected case-studies.
For the evaluation of the structural response of the buildings, structural analysis methods will be used. For RC structures the response of the load-bearing system will be simulated using models for high stain-rate impacts and/or the finite-element, FE, method. The latter will also be used for masonries, as well as failure criteria that are compatible with the FE analysis output. Where applicable, the potential for progressive collapse following local failure will be investigated through FE analysis, too. The vulnerability of the structures to landslides will be quantified using probabilistic vulnerability indices or thought probabilistic fragility curve diagrams. For the quantification of societal vulnerability a step-by-step methodology for the construction of frequency-fatalities (F-N) curves will be developed for each landslide type, using event trees and considering its dependence on structural vulnerability.'