Seminario del 2024

Febbraio
23
2024
Mauro Di Nasso
Arithmetic Ramsey theory by nonstandard methods.
nell'ambito della serie: LOGIC, CATEGORIES, AND APPLICATIONS SEMINAR
algebra e geometria
logica
In recent years there has been a growing interest in Ramsey theory and related problems in combinatorics of numbers. Historically, the earliest results in this field are Schur's Theorem ("In every finite coloring of the naturals there exists a monochromatic triple a, b, a+b") and van der Waerden's Theorem ("In every finite coloring of the naturals there exist monochromatic arithmetic progressions of arbitrary length"). A peculiar aspect of this area of research is the wide variety of methods used: in addition to the tools of elementary combinatorics, also methods of discrete Fourier analysis, ergodic theory, and ultrafilter space algebra have been successfully applied. Recently, a further line of research has been undertaken, in which combinatorial properties of sets of integers are studied by methods of nonstandard analysis. In this seminar I will discuss these methods and present some examples of their applications.
organizzato da: Martino Lupini
nell'ambito del Progetto Fondi U.E. ERC DAT CUP J33C22004270006 G.A. 101077154 DEFINABLE ALGEBRAIC TOPOLOGY del prof. Martino Lupini

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