Weighted zero-sum sequences and applications in factorization theory

活动时间： 05月06日20时00分       

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讲座内容：

Let (G,+,0) bea finite abelian group. A sequence g1 ···gkover G is called a zero-sum sequence if g1 +··· +gk= 0 (sequences that just differ by the ordering of the terms are considered asequal). For a set of weights Ω (common choices for weights are integers orendomorphisms of the group), an Ω-weighted zero-sum sequence is a sequence g1···gk over G such that w1g1+···+wkgk = 0 for some w1 ,...,wk∈ Ω. The set of zero-sumsequences over G and the set of Ω-weighted zero-sum sequences form monoids withconcatenation as operation, and various results on generalizations of classicalzero-sum constants to weighted zero-sums have been obtained in recent years.We present some results on the arithmetic of monoids of Ω-weighted zero-sum sequences.Moreover, we discuss applications of this problem to factorizations of norms ofalgebraic integers. This is joint work with S. Boukheche, K. Merito and O.Ordaz.

主讲人介绍：

WolfgangSchmid received his PhD from the University of Graz, Austria in 2003 for athesis written under the direction of Prof. Alfred Geroldinger. After severalyears as a researcher at the University of Graz, he moved to France. Currently,he is a professor of mathematics at the University of Paris 8 and a member ofthe LAGA, a joint research laboratory of the French National Centre forScientific Research (CNRS), the University Sorbonne Paris Nord, and theUniversity of Paris 8.

Theresearch interests of Wolfgang Schmid include combinatorics, commutative algebra,and number theory. He is the author of about fifty research articles and somesurvey articles in these subjects. A unifying theme of his research activitiesis a desire to understand qualitatively and quantitatively the phenomena ofnon-uniqueness of factorizations into irreducible elements in various algebraicstructures.At the University Paris 8,he is is the head of the undergraduate program of mathematics and the directorof the doctoral school CLI, which offers doctoral programs in communicationscience, computer science, engineering, linguistics, and mathematics.

发布时间：2022-05-05 11:32:41