Dipartimento di Matematica, Aula Seminari.<\/p>\n
Many theorems in combinatorics share a very similar structure: Let $M$ be monoid acting by endomorphism on a partial semigroup $S$. For each finite coloring of $S$, there are “nice” monochromatic subsets $N\\subseteq S$<\/i>. Examples of theorems of this form are Carlson\u2019s theorem on variable words, Gowers\u2019 $\\mathrm{FIN}_k$ theorem, and Furstenberg-Katznelson’s Ramsey theorem.<\/p>\n
In 2019, Solecki isolated the common underlying structure of these theorems into a formal statement. Then, he proved several results, extending all aforementioned theorems at once. He also showed that such a statement strongly depends on the algebraic structure of the monoid and on the existence of certain idempotents in a suitable compact right topological semigroup.<\/p>\n
In this talk, I will present a joint work with Eugenio Colla where we further extend the results obtained by Solecki.<\/p>\n
Further information is available on the event page<\/a> on the Indico platform.<\/p>\n","protected":false},"excerpt":{"rendered":" Many theorems in combinatorics share a very similar structure: Let $M$ be monoid acting by endomorphism on a partial semigroup $S$. For each finite coloring of $S$, there are “nice” monochromatic subsets $N\\subseteq S$. Examples of theorems of…<\/p>\n