Konferenzen zum Thema Mathematische Logik, Grundlagen der Mathematik in den Vereinigten Staaten (USA)

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AIM Workshop — Effective methods in measure and dimension
15. Aug 2022 - 19. Aug 2022 • San Jose, Kalifornien, Vereinigte Staaten
Veranstalter:
American Institute of Mathematics (AIM)
Zusammenfassung:
This workshop, sponsored by AIM and the NSF, will be devoted to effective approaches to geometric measure theory. Algorithmic Randomness and Effective Descriptive Set Theory provide a novel perspective to many concepts that are classically measure-based, such as randomness and Hausdorff dimension. A core feature of this perspective is that it links the geometric properties of a set to the logical and computational complexity of its points. The new techniques have been successfully applied to extend previous results in the area to larger classes of sets (beyond analytic), and also to shed new light on why in other cases such an extension is impossible. Examples include Marstrand's projection theorem and the capacitability of sets of real numbers. The goal of this workshop is to bring together researchers with expertise in computability, set theory, geometric measure theory, and related areas to further develop these new approaches.
Eintrags-ID:
1484254
Verwandte Fachgebiete:
2
AIM Workshop: Invariant descriptive computability theory
07. Nov 2022 - 11. Nov 2022 • San Jose, Kalifornien, Vereinigte Staaten
Veranstalter:
American Institute of Mathematics (AIM)
Zusammenfassung:
This workshop, sponsored by AIM and the NSF, will be devoted to connecting two parallel approaches towards the study of the complexity of equivalence relations. On the one hand, a popular tool for classifying equivalence relations on standard Borel spaces is Borel reducibility. Invariant descriptive set theory, centered around this notion, is a vibrant field which shows deep connections with topology, group theory, combinatorics, and ergodic theory. On the other hand, a natural effectivization of Borel reducibility, named computable reducibility, appears in computability theory. Computable reducibility has proven to be a key notion for measuring the complexity of equivalence relations on the natural numbers, with fruitful applications in a variety of fields, such as: the metamathematics of arithmetic, the study of word problems for groups, the theory of numberings, and computable model theory. Despite the analogy between Borel and computable reducibility, there has been so far little effort to directly connect techniques, knowledge, and researchers of these separate fields. To counter this lack of communication, the proposed workshop will assemble a diverse group of mathematical logicians - drawn from both experts in invariant descriptive set theory and experts in computability theory working on computable reduction - to discuss on how their tools can align.
Eintrags-ID:
1485359


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Stand vom 05. Mai 2022