Computability and Effective Constructions in Mathematics

本奖项旨在为以下人士提供差旅支持：Douglas Cenzer(佛罗里达大学)、瓦伦蒂娜·哈里扎诺夫(乔治华盛顿大学)、Julia Knight(圣母大学)、Steffen Lempp和Reed所罗门(威斯康星大学麦迪逊分校)、Andre Nies(芝加哥大学)以及Marat Arslanov(喀山州立大学)、Sergey Goncharov和Andrei Morosov(俄罗斯科学院，新西伯利亚)、Serikzhan Badaev和Mikhail Peretyat‘kin(哈萨克科学院，阿拉木图)提出的合作研究的重点是可计算性理论及其在其他领域的应用，特别是代数和模型理论。具体的研究主题包括对集合的可计算逼近的研究，代数结构表示的复杂性，有效结构上附加关系的复杂性，有效结构同构的复杂性，代数结构的计数，可计算结构的自同构群，以及在交换$p-群，可计算置换群和布尔代数中的应用

PROJECT SUMMARYThe purpose of this award is to provide travel support to allow Douglas Cenzer (University of Florida), Valentina Harizanov (George Washington University), Julia Knight (University of Notre Dame), Steffen Lempp and Reed Solomon (University of Wisconsin-Madison), and Andre Nies (University of Chicago) as well as Marat Arslanov (Kazan State University), Sergey Goncharov and Andrei Morozov (Russian Academy of Sciences, Novosibirsk), and Serikzhan Badaev and Mikhail Peretyat'kin (Kazakh Academy of Sciences, Almaty) to make one research visit each to work collaboratively with their counterparts in the other country, as well as a total of three additional trips by students.The focus of the proposed cooperative research is the theory of computability and its applications to other areas, in particular algebra and model theory. Specific research topics include the study of computable approximations to sets, the complexity of presentations of algebraic structures, the complexity of additional relations on effective structures, the complexity of isomorphisms of effective structures, numerations of algebraic structures, automorphism groups of computable structures, and applications to abelian $p$-groups, to groups of computable permutations, and to Boolean algebras