[Turkmath:7954] CAHİT ARF LECTURE 2011

[Gulin Ercan]

Değerli Liste Üyeleri,

CAHIT ARF LECTURE 2011 ile ilgili bilgiyi dikkatinize sunuyoruz.

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Tarih:  24 Kasim 2011

Zaman:  15.40

Yer:  ODTU Matematik Bolumu, Cahit Arf Salonu

Konusmaci:  Jonathan Pila, Mathematical Institute, University of Oxford

Başlık:   Diophantine geometry via o-minimality

Özet:

The talk will be about an application of mathematical logic to certain
Diophantine problems.

Diophantine geometry traditionally considers rational points on
algebraic varieties. I will describe some results about the distribution
of rational points on certain non-algebraic  sets in real space which were
developed in rough analogy with ideas in Diophantine geometry.
  The starting point was a result, obtained jointly with Bombieri, that
rational points on the graph of a  real-analytic but non-algebraic
functions  are ``sparse'' in a suitable sense.   This may be generalised
to a result,
obtained with Wilkie, applicable to sets that are  ``definable  in an
o-minimal structure over the real field''. I will define this notion,
which comes from  model theory, and explain why this is the natural
setting.  The result may be applied to certain Diophantine problems, using
a strategy  proposed by Zannier in the context of the Manin-Mumford
conjecture.
I will describe this and some further applications of this strategy to
cases of the  Andre-Oort and Zilber-Pink conjectures.
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Saygılarımızla

Düzenleme Komitesi:

Gülin Ercan, Semra Öztürk Kaptanoğlu, Ahmet İrfan Seven, Cem Tezer






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