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    Eventi Dipartimento
    20.05.2019 2:30 pm - 3:30 pm



    Lunedì 20 maggio, alle ore 14:30, nell'aula G (ex Psicologia) del Dipartimento di Matematica e Fisica della Università degli Studi della Campania “Luigi Vanvitelli”, il Professore Mauro Di Nasso della Università di Pisa, terrà un seminario dal titolo 

    « Nonstandard Models in Combinatorics and Ramsey Theory»

    ABSTRACT: I will briefly recall some basic results in combinatorics and Ramsey Theory and present a new technique that is grounded on the use of nonstandard models of the integers.

    In the second part of the talk, I will focus on the (discrete) topological dynamics as given by the hypernatural numbers endowed with the shift operator, and use it to prove two classic results in Ramsey Theory. Precisely, I will give a nonstandard proof of Hindman's Theorem: "For every any finite coloring of the natural numbers there exists an infinite set X with the property
    that all possible sums of its elements have the same color"; and a new "dynamical" proof of van der Waerden's Theorem: "In any finite coloring of the natural numbers there exist monochromatic arithmetic progressions of arbitrary length".

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