Hyperk\"ahler torsion structures invariant by nilpotent Lie groups

We study HKT structures on nilpotent Lie groups and on associated nilmanifolds. We exhibit three weak HKT structures on $\R^8$ which are homogeneous with respect to extensions of Heisenberg type Lie groups. The corresponding hypercomplex structures are of a special kind, called abelian. We prove that on any 2-step nilpotent Lie group all invariant HKT structures arise from abelian hypercomplex structures. Furthermore, we use a correspondence between abelian hypercomplex structures and subspaces of ${\frak sp}(n)$ to produce continuous families of compact and noncompact of manifolds carrying non isometric HKT structures. Finally, geometrical properties of invariant HKT structures on 2-step nilpotent Lie groups are obtained.Comment: LateX, 12 page

Aging and Brain Deterioration

Carlos Dotti and Vicente Rodríguez (coordinators).Advanced age significantly increases the risk of developing chronic diseases such as cancer, diabetes, cardiovascular, immune and mental disease. Regarding the latter, advanced age is a necessary factor for the development of non-hereditary forms of neurodegenerative diseases such as Alzheimer’s and Parkinson’s. Despite years of intense research, we still do not know how these diseases occur, this being one of the main reasons for the lack of adequate interventions to prevent or cure these pathologies. To overcome the current limitations in the field, we plan to: 1) generate basic knowledge on the mechanisms responsible for cognitive, behavioral, motor, metabolic and sociability disorders that occur with age, 2) define the mechanisms that determine individual susceptibility to neurodegeneration, 3) design and develop strategies to improve brain aging, and 4) explore social and environmental conditions of the older population to know their influence in brain degeneration. Individual, social and policy interventions must be considered for future research.Peer reviewe

Tetraspanin 6: A novel regulator of hippocampal synaptic transmission and long term plasticity

Tetraspanins (Tspan) are transmembrane proteins with important scaffold and signalling functions. Deletions of Tetraspanin 6 (Tspan6) gene, a member of the tetraspanin family, have been reported in patients with Epilepsy Female-restricted with Mental Retardation (EFMR). Interestingly, mutations in Tspan7, highly homologous to Tspan6, are associated with X-linked intellectual disability, suggesting that these two proteins are important for cognition. Considering recent evidences showing that Tspan7 plays a key role in synapse development and AMPAR trafficking, we initiated the study of Tspan6 in synaptic function using a Tspan6 knock out mouse model. Here we report that hippocampal field recordings from Tspan6 knock out mice show an enhanced basal synaptic transmission and impaired long term potentiation (LTP). A normal paired-pulse facilitation response suggests that Tspan6 affects the properties of the postsynaptic rather than the presynaptic terminal. However, no changes in spine morphology or postsynaptic markers could be detected in Tspan6 KO mice compared with wild types. In addition, Tspan6 KO mice show normal locomotor behaviour and no defects in hippocampus-dependent memory tests.Fund for Scientific Research Flanders (FWO) grant; KU Leuven; Flemish Institute for Biotechnology (VIB), IUAP (P7/16).Peer Reviewe