COMUNICAZIONI

Da Giovedì 10 a domenica 13 Febbraio: AILA2005 XXII Incontro di Logica Matematica L'incontro ha lo scopo di rappresentare la ricerca logica in Italia nelle sue varie articolazioni e costituire un momento di incontro e aggregazione per la comunità logica italiana. Per il programma e altre informazioni sul convegno: http://www.dm.unipi.it/~aila2005

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mercoledì 16-02-2005 (16:00) - Aula Magna Renling Jin (Charleston, U.S.A) : Colloquium Dipartimento di Matematica :Magic of Infinitely Large Integers

In a nonstandard model we have many integers, which are greater than all known positive integers in our standard world. Are these integers purely for a mind game or useful tools for understanding our standard world of numbers? In the talk, the speaker will present some of his results that illustrate how these infinitely large integers are used for obtaining new standard theorems in combinatorial number theory. For example, he recently derived a theorem on Freiman's inverse problems that if A+A is small, then A must have some arithmetic structure. Freiman's inverse problems have been popular research topics in combinatorial number theory since 1960s. The theorem characterizes the arithmetic structure of A when the size of A+A is 3 times the size of A plus b, where b can be, for example, any constant integer independent of the size of A. The best results before the speaker's work had been for b < -1. The audience will not be assumed to have prior knowledge of nonstandard models. Any people above undergraduate math level should be able to understand the questions and theorems without difficulty.

Giulia Curciarello Segreteria Didattica tel: 050-2213219 e-mail curciare@dm.unipi.it

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