Computability and Effective Constructions in Mathematics

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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