• Datum: –12.00
  • Plats: Polacksbacken ITC1112
  • Föreläsare: Michael Björklund, Chalmers
  • Arrangör: Matematiska institutionen
  • Kontaktperson: Anders Öberg
  • Seminarium

Central limit theorems in geometry of numbers

Abstract: It is a popular problem in number theory to consider the asymptotics of the number of points  in the intersections of a (random) lattice with a sequence of growing bodies in Euclidean space. One knows that in great generality, this count is proportional to the volumes of the bodies, with error terms of sizes roughly the square roots of the volumes. It is therefore natural to expect that (at least under some additional assumptions) a central limit theorem for the counts also holds. 

The aim of this talk is to survey some recent preprints, jointly written with A. Gorodnik (Bristol), that establishes such central limit theorems in various instances.  Although our main tools are dynamical,  people in probability theory might still enjoy our use of a “relativization” of the classical “Method of cumulants” which will be explained during the talk.