BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Luca San Mauro (Institute for Discrete Mathematics and Geometry) DTSTART:20210302T130000Z DTEND:20210302T140000Z DTSTAMP:20260423T005700Z UID:CTA/51 DESCRIPTION:Title: Cla ssifying word problems\nby Luca San Mauro (Institute for Discrete Math ematics and Geometry) as part of Computability theory and applications\n\n \nAbstract\nThe study of word problems dates back to the work of Dehn in \ n1911. Given a recursively presented algebra A\, the word problem of A is \nto decide if two words in the generators of A refer to the same element. \nNowadays\, much is known about the complexity of word problems for \nal gebraic structures: e.g.\, the Novikov-Boone theorem – one of the most \ nspectacular applications of computability to general mathematics – \nst ates that the word problem for finitely presented groups is \nunsolvable. Yet\, the computability theoretic tools commonly employed to \nmeasure the complexity of word problems (e.g.\, Turing or m-reducibility) \nare defin ed for sets\, while it is generally acknowledged that many \ncomputational facets of word problems emerge only if one interprets them \nas equivalen ce relations.\nIn this work\, we revisit the world of word problems throug h the lens of \nthe theory of equivalence relations\, which has grown imme nsely in recent \ndecades. To do so\, we employ computable reducibility\, a natural \neffectivization of Borel reducibility.\nThis is joint work wit h Valentino Delle Rose and Andrea Sorbi.\n LOCATION:https://researchseminars.org/talk/CTA/51/ END:VEVENT END:VCALENDAR