报告人：P. Ara 教授
报告人简介：Pere Ara,西班牙巴塞罗那自治大学教授，研究领域为环论、半群理论等，已在知名期刊Adv. Math., Trans. Amer. Math. Soc., Israel. J. Math., J. Algebra等杂志上发表100余篇论文，目前担任J. Algebra Appl.期刊的编委。
报告一：Free actions of groups on separated graph-algebras
报告简介：In this talk, we study free actions of groups on separated graphs and their -algebras, generalizing previous results involving ordinary (directed) graphs.
We prove a version of the Gross-Tucker Theorem for separated graphs yielding a characterization of free actions on separated graphs via a skew product of the (orbit) separated graph by a group labeling function.
报告二：Leavitt path algebras of weighted and separated graphs
报告简介：In this talk,we show that Leavitt path algebras of weighted graphs and Leavitt path algebras of separated graphs are intimately related.
报告三：The type semigroup, comparison, and almost finiteness for ample groupoids
报告简介：We prove that a minimal second countable ample groupoid has dynamical comparison if and only if its type semigroup is almost unperforated. Moreover, we investigate to what extent a not necessarily minimal almost finite groupoid has an almost unperforated type semigroup. Finally, we build a bridge between coarse geometry and topological dynamics by characterizing almost finiteness of the coarse groupoid in terms of a new coarsely invariant property for metric spaces, which might be of independent interest in coarse geometry. As a consequence, we are able to construct new examples of almost finite principal groupoids lacking other desirable properties, such as amenability or even a-T-menability. This behaviour is in stark contrast to the case of principal transformation groupoids associated to group actions.
报告四：The Groupoids of Adaptable Separated Graphs and Their Type Semigroups
报告简介：Given an adaptable separated graph, we construct an associated groupoid and explore its type semigroup. Specifically, we first attach to each adaptable separated graph a corresponding semigroup, which we prove is an -unitary inverse semigroup. As a consequence, the tight groupoid of this semigroup is a Hausdorff etale groupoid. We show that this groupoid is always amenable and that the type semigroups of groupoids obtained from adaptable separated graphs in this way include all finitely generated conical refinement monoids. The first three named authors will utilize this construction in forthcoming work to solve the realization problem for von Neumann regular rings, in the finitely generated case.
报告五：Refinement monoids and adaptable separated graphs
报告简介：We define a subclass of separated graphs, the class ofadaptable separated graphs, and study their associated monoids. We show that these monoids are primely generated conical refinement monoids, and we explicitly determine their associatedI-systems. We also show that any finitely generated conical refinement monoid can be represented as the monoid of an adaptable separated graph. These results provide the first step toward an affirmative answer to the Realization Problem for von Neumann regular rings, in the finitely generated case.