Seminario di algebra e geometria, logica
ore
14:00
presso Seminario II
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.