[Liste-CICMA] Margaret Thomas (McMaster) at McGill on March 20

Guillermo Martinez-Zalce martinez at crm.umontreal.ca
Tue Mar 13 10:38:14 EDT 2018


20 March 2018, McGill University. Burnside Hall, room 920
2:30 - 3:30   Margaret Thomas (McMaster) 
Counting rational points on definable sets 
Abstract <http://www.math.mcgill.ca/rags/seminar/Thomas-200318.html> 

The results outlined in this talk are part of a wider, flourishing interaction between diophantine geometry and model theory. The central aim is to bound the density of rational and algebraic points lying on certain `transcendental' subsets of the reals, with a view to diophantine applications. Following influential work by Pila and Wilkie in this area (which has had stunning number-theoretic applications e.g. to the Manin-Mumford and André-Oort Conjectures), our focus is on sets which are first-order definable in various `o-minimal' expansions of the real field. We shall survey background and some results in this area, in particular concerning possible improvements to the bound given by Pila and Wilkie. These include instances of a conjecture of Wilkie, which proposes an improvement for the real exponential field, and some recent progress made towards finding an effective version of the Pila-Wilkie Theorem.
____________________
Guillermo Martinez-Zalce
Responsable des laboratoires
Centre de recherches mathématiques
Université de Montréal
Case postale 6128, Succursale centre-ville
Montréal (Québec)
H3C 3J7
tel: (514) 343-7574
      (514) 398-3826 (mercredis)


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