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Forthcoming events in this series
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"Higher amalgamation and definable groupoids" (after Hrushovski and Goodrick-Kolesnikov)
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Model Theory of the ring of adeles
Abstract
I shall discuss joint work with Angus Macintyre on the model theory of the ring of adeles of a number field
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Finite Fields and Model Theory
Abstract
I will discuss some theorems of Chatzidakis, van den Dries, and Macintyre on definable sets over finite fields (Crelle 1992). This includes a geometric decomposition theorem for definable sets and a generalization of the Lang-Weil estimates, and uses model theory of finite and pseudo-finite fields.
If time permits, I shall mention a recent application of this work by Emmanuel Kowalski on new bounds for exponential sums (Israel Journal of Math 2007).
I would also like to mention some connections to the model theory of p-adic and motivic integrals and to general problems on counting and equidistribution of rational points.
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