Midwest Computability Seminar

Part i

The Midwest Computability Seminar is meeting remotely in the winter and spring of 2021. The recurring Zoom link is:


Meeting ID: 997 5433 2165

Passcode: midwest

slides    Panopto video     YouTube video

This session will be held jointly with the Computability Theory and Applications Online Seminar.

DATE: Monday, February 1st, 2021

TIME: 3:30 - 4:30 PM Central Time

SPEAKER: Arno Pauly - Swansea University

The structure of Weihrauch degrees - what we know and what we don't know

The Weihrauch degrees are a popular setting for classifying the computational content of mathematical theorems. Understanding their structure is useful as technical tool in concrete classifications. Moreover, their structure tells us something about how degrees of non-computability look like in principle. In this talk, I'll summarize what is already known about the structure of the Weihrauch degrees, and try to draw attention to some open problems. For example. we know that they form a distributive lattice, which is not a Heyting algebra and which is not complete. We have further natural algebraic operations, and we know of a few that they are definable in terms of others. The Medvedev degrees embed into the Weihrauch degrees as a lattice, as do the many-one degrees (but in a weird way).

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