ULTRA-COMBINATORICS. Applications of ultrafilters in combinatorial number theory, and related topics
timetable:
Thu 24 Jan, 17:10 - 17:50, Aula Dini
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Partition Regularity of Nonlinear Polynomials
speaker: Lorenzo Luperi Baglini (Università di Pisa)abstract: We say that a polynomial $P(x{1},...,x{n})$ (with coefficients in $\mathbb{Z}$) is partition regular on $\mathbb{N}=\{1,2,...\}$ if whenever the natural numbers are finitely colored there is a monochromatic solution to the equation $P(x{1},...,x{n})=0$. While the linear case has been settled by Richard Rado almost a century ago, not very much is known for nonlinear polynomials. Using a technique that mixes ultrafilters and nonstandard analysis, we prove that the partition regularity can be ensured for the elements of two "natural" classes of nonlinear polynomials.
timetable:
Thu 24 Jan, 17:10 - 17:50, Aula Dini
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