SM: Arithmetic Groups and Their Applications in Combinatorics, Geometry and Topology

将于4月15日至18日在夏洛茨维尔的弗吉尼亚大学校园举办一个名为“算术小组及其在组合学、几何学和拓扑学中的应用”的研讨会。研讨会的科学计划将由来自美国、巴西、法国和以色列的该领域领先专家的讲座组成，并将突出过去几年取得的最重大成果。将特别关注算术群的结构性质的分析(第一Betti数的虚正性、同余子群问题、有界生成)，它们在代数几何(伪射影平面和其他重要代数簇的伪版本)、微分几何和拓扑学(双曲3-流形、等谱局部对称空间)和组合学(构造展开器)中的应用。算术群是元素是具有整数项的矩阵的特殊群。这个概念可以追溯到高斯关于积分二次型的工作，在数学的许多领域，包括代数和数论的各个部分(例如，自同构形理论)，都发挥着至关重要的作用。近年来，算术群理论在代数和微分几何、李理论和组合学中出现了新的应用。研讨会将展示涉及算术小组的重要成果。重点将放在使在各种领域工作的研究人员，特别是年轻研究人员，能够使用算术小组理论的方法。

A workshop ``Arithmetic Groups and Their Applications in Combinatorics, Geometry and Topology" will be held April 15-18 on the campus of the University of Virginia in Charlottesville. The scientific program of the workshop will be composed of lectures delivered by the leading experts in the area from the US, Brazil, France and Israel, and will highlight the most significant results obtained in the last few years. Special attention will be given to such topics as the analysis of structural properties of arithmetic groups (virtual positivity of the first Betti number, congruence subgroup problem, bounded generation), their applications in algebraic geometry (fake projective planes and fake versions of other important algebraic varieties), in differential geometry and topology (hyperbolic 3-manifolds, isospectral locally symmetricspaces) and in combinatorics (construction of expanders).Arithmetic groups are special groups whose elements are matrices with integral entries. This notion, which can be traced back to the work of Gauss on integral quadratic form, plays a crucial role in many areas of mathematics including algebra and various parts of number theory (e.g., the theory of automorphic forms). In recent years, new applications of the theory of arithmetic groups have emerged in algebraic and differential geometry, Lie theory and combinatorics. The workshop will showcase important results involving arithmetic groups. The focus will be placed on making the methods of the theory of arithmetic groups accessible to researchers, particularly young ones, working in a variety of areas.