Workshop on the Extended Family of R. Thompson Groups.

该项目是一个研讨会，主要关注R的扩展家族理论。汤普森集团本文报道了R.汤普森群是一类重要的（一般）双表示单群（或近似单群），其中包含了第一个已知的双表示无限单群的例子。这个家族的理论以令人惊讶和深刻的方式与其他数学领域交叉;为逻辑等领域的问题提供了例子和反例。J. Thompson），solvable and unsolvable problems in group theory（R. J. Thompson和R. McKenzie），同伦和范畴论（P. Freyd and A. Heller）、形状理论（J. Hastings）、Teichmuller理论和映射类群（R.该研讨会将有助于教育新的和建立的研究人员在这个动态领域的艺术状态，以及突出这些群体的理论和数学的其他领域之间的许多联系。特别是，研讨会将举办三个小型课程的连接的大家庭的R。汤普森小组的各种数学的外向领域。这些研讨会的题目和主持人如下：1）半群，'etale拓扑群胚，C*-代数和Thompson群; Mark V. Lawson; 2）Thompson群的辫子，逻辑和几何表示;帕特里克Dehornoy; 3）Thurston的分段积分射影群;弗拉基米尔塞尔吉斯库。讲习班还将举办一个问题会议，重点是这些群体和与他们有关的更广泛的主题，并将在专题研究期刊上发表小型课程和问题讨论的摘要。

The proposed project is a workshop, with primary focus the theory of the extended family of R. Thompson groups. The extended family of R. Thompson groups are an important family of (generally) finitely presented simple groups (or, nearly simple) which contain the first known examples of finitely presented infinite simple groups. The theory of this family intersects other areas of mathematics in often surprising and profound ways; providing examples and counterexamples to questions from areas such as logic (R. J. Thompson), solvable and unsolvable problems in group theory (R. J. Thompson and R. McKenzie), homotopy and category theory (P. Freyd and A. Heller), shape theory (J Dydak and H. Hastings), Teichmuller theory and mapping class groups (R. Penner) and various other areas as well.The workshop will serve to both educate new and established researchers on the State of the Art in this dynamic area, as well as highlight some of the many connections between the theory of these groups and other areas of Mathematics. In particular, the workshop will host three mini-courses on the connections of the extended family of the R. Thompson groups to various outward-reaching areas of mathematics. The titles and presenters of these workshops are given below:1) Semigroups, 'etale topological groupoids, C*-algebras, and Thompson groups; Mark V. Lawson.2) Braids, logic and geometric presentations for Thompson's groups; Patrick Dehornoy.3) Thurston's piecewise integral projective groups; Vladimir Sergiescu.The workshop will also host a problem session focussing on these groups and the broader topics associated with them, and will publish summaries of the minicourses and the problem session discussion in a topical research journal.