Monoids of graph agglomerations and lattices over Bass rings

主 讲 人 ：Daniel Smertnig    

活动时间：05月13日20时00分    

地      点 ：会议链接：https://zoom.us/j/97859517195?pwd=TkQ4QitMWmsvMUV4dFBvYWhlM3Q3QT09; 会议号：97859517195 密码：771142

讲座内容：

Given a finite graph G withvertex set V andedge set E,we define an agglomeration to be a function a: V ∪E → N0 such that a(v) ≥ a(e) whenever v ∈ V ande ∈ E areincident. The set of all agglomerations on a fixed graph forms a Diophantine monoid(and therefore in particular a Krull monoid). We shall discuss basic propertiesof monoids of graph agglomerations and show how their arithmetical propertiesare linked to graph-theoretic properties of the underlying graph. Monoids ofgraph agglomerations arise in the study of the monoid of lattices over Bassrings, and can therefore be used to study direct-sum decompositions of latticesover such rings.

主讲人介绍：

Daniel Smertnig received his PhD from theUniversity of Graz (Austria) in 2014. After a postdoc at Dartmouth College(USA) and the University of Waterloo (Canada), he is currently a professor foralgebra at the University of Graz (interim appointment).

发布时间：2022-05-12 19:23:21