Mixed Hodge structures and vector bundles on the projective Plane I

We describe an equivalence of categories between the category of mixed Hodge structures and a category of vector bundles on the toric complex projective plane which verify some semistability condition. We then apply this correspondence to define an invariant which generalises the notion of R-split mixed Hodge structure and compute extensions in the category of mixed Hodge structures in terms of extensions of the corresponding vector bundles. We also give a relative version of this correspondence and apply it to define stratifications of the bases of the variations of mixed Hodge structure.

Embedding theorems of function classes, I

"Vegeu el resum a l'inici del document del fitxer adjunt."

Sabbatical stay at CREVER, University Rovira i Virgili

A three-year research proposal of international impact and quality was developed between the author and CREVER researchers, taking into account the infrastructure and research lines already being carried out at CREVER. The project is related to the study of new mixtures in thermal activated systems, by the addition of a third component to help the heat transfer processes. The project proposes the use of water and lithium nitrate as absorbents in ternary ammonia mixtures, varying the concentration with the objective of optimising the mixture for solar air conditioning purposes. Also, the research proposal will promote an intensive collaboration in the following years between CREVER and The Centro de Investigación en Energía-UNAM, Mexico.