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.
交通：阪急六甲駅またはJR六甲道駅から神戸市バス36系統「鶴甲団地」 行きに乗車，「神大本部工学部前」停留所下車，徒歩すぐ． http://www.kobe-u.ac.jp/info/access/rokko/rokkodai-dai2.htm
連絡先：ブレンドレ ヨーグ [email protected]