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MIMS

Programme

  Monday Tuesday Wednesday Thursday Friday
10:00-11:00 Wilkie Wilkie Wilkie Pila Habegger
11:00-11:30     Break    
11:30-12:30 Wilkie Pila Habegger Habegger Free
12:30-13:30     Lunch    
13:30-14:30 Pila Wilkie Pila Pila Habegger
14:30-15:30 Habegger Masser Jones Yafaev Finish
15:30-16:00     Break    
16:00-17:00 Tutorial Tutorial Tutorial Tutorial  

 

Courses

 

Guest Lectures

David Masser
Relative Manin-Mumford for abelian varieties

Abstract:
With an eye or two towards applications to Pell's equation and Davenport's work on integration of algebraic functions, Umberto Zannier and I have recently characterised torsion points on a fixed algebraic curve in a fixed abelian scheme of dimension bigger than one (when all is defined over the algebraic numbers): there are at most finitely many provided the natural obstacles are absent. I sketch the proof as well as the applications.

Andrei Yafaev
Hyperbolic Ax-Lindemann-Weierstrass theorem

Abstract:
This is a joint work with B. Klingler and E. Ullmo. We generalise the definability result of Peterzil and Starchenko to general Shimura varieties and prove the general hyperbolic Ax-Lindemann-Weierstrass theorem.

Gareth Jones
Integer valued definable functions

Abstract:
Wilkie has conjectured that for sets definable in the real field with exponentiation, the bound in the Pila-Wilkie theorem can be improved to a power of log H. At present this is only known for curves and certain surfaces. An easy consequence of the result for curves is that a definable analytic function on the real line that takes integer values at all natural numbers either grows faster than exp(x^epsilon) for some positive epsilon or is a polynomial. This can be thought of as a (rather weak) analogue of Polya's theorem on integer valued entire functions. I'll discuss the above and then show how some simple o-minimality arguments can be used to extend this result to functions of several variables.

Last modified: August 27, 2013 12:04:58 PM BST.

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