Bar-Ilan Algebra Seminar ========================================= Date: Wednesday, December 15, 2010 / 8 Tevet 5771 Time: 10:30 am promptly Place: Third floor seminar room, Mathematics building Speaker: Tomer Schlank (Hebrew University of Jerusalem) Title: Homotopy theory and solubility of Diophantine equations Abstract: A classical problem in number theory is to determine whether or not a system of polynomial equations E has a rational solution. If there is such a solution one can always present it. But to prove that no solution exists might be a more delicate issue. For this one uses the notion of obstructions. In the talk I would present a way to construct such obstructions based on exploring some kind of topological realization of E called "The \'{e}tale homotopy type", which was defined by Artin and Mazur. It turns out that this method of constructing obstructions can recover many of previously known obstructions (e.g the the Brauer -Manin, the \'{e}tale-Brauer and certain descent obstructions.) and thus give those obstructions a topological interpretation and shed light on the relationships between them. This is a joint work with Y.Harpaz. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Michael Schein <mschein@math.biu.ac.il>