Arithmetic Geometry Year
Poncelet French-Russian Laboratory,
2012 - 2013
Aurélien Galateau (University of Besançon)
Marc Hindry (University of Paris 7, Laboratoire Poncelet)
Philippe Lebacque (University of Besançon)
Michael A. Tsfasman (Laboratoire Poncelet, Institute for Information Transmission Problems)
Alexey Zykin (National Research University Higher School of Economics, Laboratoire Poncelet, IITP)
Arithmetic geometry is a central area of research in modern mathematics deeply connected to almost all of its branches. There are many different approaches to the field, that use a wide variety of techniques. Complex, real, p-adic analysis, algebraic geometry, algebraic number theory, group theory, representation theory, combinatorics, the theory of differential equations and dynamical systems, topology and differential geometry all play important roles.
Arithmetic geometry typically deals with questions of the form: "Does a given variety have integer (rational) points? If yes, how many?" Even a quick glance at the theory of elliptic curves, at Faltings theorem or at the Fermat's last theorem give a thorough impression of the mathematical wealth of this research area.
Mathematical activities during the semester include a weekly arithmetic seminar, courses given by internationally renown researchers and three conferences. The first conference will be devoted to zeta functions, the second one to arithmetic geometry and the third one to global fields and varieties over them.