报告题目：Gr\{u}nwald Version of Van der Waerden's Theorem for Semimodules

报告人：南京大学 代雄平教授

时间：1月18日(周一)10:00-11:00

地点：管研楼1518

摘要：Let $(G,+)$ be any given semimodule over a discrete semiring $(R,+,\cdot)$ with a finite coloring, say $G=B_1\cup\dotsm\cup B_q$.

By establishing a Regional Multiple Recurrence Theorem for semimodules, we prove that one of the colors $j$ has the property that if $F\subseteq G$ is any finite set, then one can find some ``syndetic'' subset $D_F$ of $(R,+)$ such that for each $d\in D_F$ there is some $a\in B_j$ with $a\pmb{+}dF\subseteq B_j$. This in turn implies that each Bohr almost point is multiply uniformly recurrent.

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