Videos

Algebraic Dynamics, 10

August 3, 2012
Keywords:
  • o-minimality
  • model theory
  • semi-algebraic geometry
  • semi-algebraic sets
  • quantifier elimination
  • totally real fields
  • algebraic dynamics
  • Pila-Wilkie theorem
MSC:
  • 03C10
  • 03C05
  • 03C64
  • 03C60
  • 03C50
  • 03C40
  • 03Cxx
  • 03-xx
  • 12D15
  • 12Dxx
Abstract
The workshop will consist of two minicourses, together with a selection of topical lectures. In the model theory course, o-minimality, and specifically the concrete example of the semi-algebraic sets of real numbers will provide the setting in which we introduce various fundamental results from model theory. The algebraic dynamics course will allow the introduction of concepts and proof techniques from number theory and algebraic geometry in the context of applications involving model theory. Toward the end of the workshop, the two minicourses will converge on the Pila-Wilkie theorem concerning points on analytic varieties, a result crucial in recent applications of o-minimality to diophantine geometry.