Recursion Theory and its Applications (23w5039)

The Institute for Advanced Study in Mathematics will host the "Recursion Theory and its Applications" workshop in Hangzhou, China from October 15 to October 20, 2023.

Recursion theory measures the complexity of mathematical objects in terms of what is computable, in other words, what can be determined by a computer with no space or time limitations. We can define, for example, computable sets of natural numbers, computable (continuous) functions on the real numbers, or computably enumerable open subsets of the reals. Adding an oracle---an outside source of information---allows us to extend the reach of recursion theory beyond the computable. For example, every continuous function on the real numbers is a computable function relative to some oracle. For another example, a set of real numbers has Hausdorff dimension zero if and only if there is an oracle relative to which every real in the set can be significantly compressed. In this way, recursion theory offers a fine-grained way to analyze some of the most central notions in mathematics. This has recently led to deep applications to analysis, number theory, and set theory. The focus of this workshop is on understanding and extending these applications of recursion theory.

The Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).