In this document, I briefly describe the projects that I am currently working on. More technical details may be found in my grant proposal to the National Science Foundation, which was approved, and may be found at: http://www.math.fsu.edu/~agashe/info.html. My past research is summarized in the document “Past research”, which may be found at the same website. My current research is in Arithmet...

Il s’agit d’un patient de 47 ans, ayant comme antécédent une ponction biopsie prostatique il ya 3 mois. Le patient consulte pour des douleurs du bas du dos d’aggravation rapidement progressive avec apparition depuis une semaine des lombosciatalgies bilatérales mal systématisées. L’examen clinique trouve un patient apyrétique, sans déficit sensitivomoteur ni troubles sphinctériens. L’examen du r...

In this thesis I will describe an explicit method for performing an 8-descent on elliptic curves. First I will present some basics on descent, in particular I will give a generalization of the definition of n-coverings, which suits the needs of higher descent. Then I will sketch the classical method of 2-descent, and the two methods that are known for doing a second 2-descent, also called 4-des...

Let Y C Pm be a subvariety of codimension d defined by an ideal / in charp > 0 with //'(Y, 0 (-1)) = 0. If t is an integer greater than log (d) and Hi( Y, f/l"+i) = 0 for n » 0 and i =1,2, then Pic(Y) is an extension of a finite p-primary group of exponent at most pt by Z[ 0 (1 )1 and Br'(Y)(p) is a group of exponent at most pl'. If Y is also smooth and defined over a finite field with dim Y < ...

Forty native Mediterranean plant species were screened for emissions of the C5 and C10 hydrocarbons, isoprene and monoterpenes, in five different habitats. A total of 32 compounds were observed in the emissions from these plants. The number of compounds emitted by different plant species varied from 19 (Quercus ilex) to a single compound emission, usually of isoprene. Emission rates were normal...

Ecosystem invasion by non-native, nitrogen-fixing species is a global phenomenon with serious ecological consequences. However, in the Mediterranean basin few studies addressed the impact of invasion by nitrogen-fixing shrubs on soil quality and hydrological properties at local scale, and the possible effects on succession dynamics and ecosystem invasibility by further species. In this multidis...

The use of ecohydrologically suitable microsites, such as sink patches (i.e. zones intercepting and infiltrating runoff) nurse shrubs, have largely been proposed tools to improve the establishment late-successional trees in Mediterranean reclaimed landscapes. Nonetheless, this technique needs be accurately tested along with influence seedling water-use strategy. To that purpose, we monitored sh...