Kommende Vorträge

Contact: Pieter Moree (moree @ mpim-bonn.mpg.de)

A theorem of Serre states that almost all plane conics over Q have no rational point. We prove an analogue of this for a family of conics parametrised by certain elliptic curves using elliptic divisibility sequences and a version of the Selberg sieve. Another way to think about this result is: we show that 0% of points on elliptic curves have a denominator which is a sum of two squares.

Contact: Aru Ray (aruray @ mpim-bonn.mpg.de)

We consider the Euler characteristics of closed orientable 2n-manifolds with a given fundamental group G, and highly-connected universal cover. We  strengthen the 4-dimensional Hausmann-Weinberger estimates and extend to higher dimensions.  As an application we obtain new restrictions for non-abelian finite groups arising as fundamental groups of rational homology 4-spheres.

Given a Lie algebroid structure on a vector bundle $A$ and a leaf $L$ of this Lie algebroid, a natural question is whether all nearby Lie algebroid structures on A have a leaf which is diffeomorphic to $L$. This question was answered by M. Crainic and R. Fernandes.