Kobe Colloquium on Logic, Statistics and Informatics
以下の要領でコロクウィウムを開催します。
日時：2010年12月16日（木）15:10 〜
場所：神戸大学自然科学総合研究棟3号館4階421室（渕野グループプレゼンテーション室）講演者：Dmitri Shakhmatov（愛媛大学）
題目：A Kronecker-Weyl theorem for subsets of abelian groups
アブストラクト：
Let N be the set of non-negative integer numbers, T the circle group and c the cardinality of the continuum.
Given an abelian group G of size at most 2^c and a countable family F of infinite subsets of G,
we construct ``Baire many'' monomorphisms pi: G to T ^c such that pi(E) is dense in { y in T^c : ny=0 }
whenever n in N , E in F, nE = {0} and { x in E : mx=g } is finite for all g in G and m such that
n = mk for some k in N \ {1} . We apply this result to obtain an algebraic description of countable
potentially dense subsets of abelian groups, thereby making a significant progress towards a
solution of a problem of Markov going back to 1944. A particular case of our result yields a
positive answer to a problem of Tkachenko and Yaschenko (2002). Applications to group actions and
discrete flows on T^cont, diophantine approximation, Bohr topologies and Bohr compactifications
are also provided.