BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Arno Pauly (Swansea University) DTSTART:20210201T213000Z DTEND:20210201T223000Z DTSTAMP:20260423T005728Z UID:CTA/42 DESCRIPTION:Title: The structure of Weihrauch degrees - what we know and what we don't know\ nby Arno Pauly (Swansea University) as part of Computability theory and ap plications\n\n\nAbstract\nThe Weihrauch degrees are a popular setting for classifying the computational content of mathematical theorems. Understand ing their structure is useful as technical tool in concrete classification s. Moreover\, their structure tells us something about how degrees of non- computability look like in principle. In this talk\, I'll summarize what i s 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 c omplete. We have further natural algebraic operations\, and we know of a f ew 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).\n LOCATION:https://researchseminars.org/talk/CTA/42/ END:VEVENT END:VCALENDAR