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DTSTAMP:20250716T232332Z
DESCRIPTION:Counting rational points on definable sets\n\nThe results outli
 ned in this talk are part of a wider\, flourishing interaction between dio
 phantine geometry and model theory. The central aim is to bound the densit
 y of rational and algebraic points lying on certain `transcendental' subse
 ts of the reals\, with a view to diophantine applications. Following influ
 ential work by Pila and Wilkie in this area (which has had stunning number
 -theoretic applications e.g. to the Manin-Mumford and André-Oort Conjectur
 es)\, our focus is on sets which are first-order definable in various `o-m
 inimal' expansions of the real field. We shall survey background and some 
 results in this area\, in particular concerning possible improvements to t
 he 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 th
 e Pila-Wilkie Theorem.\n
DTSTART:20180320T183000Z
DTEND:20180320T193000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Margaret Thomas\, McMaster
URL:/mathstat/channels/event/margaret-thomas-mcmaster-
 285889
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