BEGIN:VCALENDAR VERSION:2.0 CALSCALE:GREGORIAN PRODID:iCalendar-Ruby BEGIN:VEVENT CATEGORIES:Lectures & Presentations DESCRIPTION:Mathematics Ph.D. candidate Mohmmad Zailai defends his disserta tion on "Topological Field Theories with Defects" on March 1 at 10:30 a.m. via Teams.\n\n \n\nJoin on Teams. \n\nThe dissertation committee is Alexei Davydov\, Vladimir Uspenskiy\, Marcel Bischoff\, and Nancy Sandler.\n\nAbst ract: Topological field theories are important due to their numerous applic ations in theoretical physics and modern mathematics. A useful way to study topological field theories is by using category theory. In this dissertati on we considered different types of topological filed theories in dimension two. R.Dijkraaf found that the category 2Cobc of surfaces is free on a com mutative Frobenius algebra. G.Segal and G.Moore showed that the category 2C obo-c of open surfaces is described by a Cardy pair. We extended these resu lts to the following: the category 2Cob2o of two coloured ribbon graphs is free on a pair of Frobenius algebras and a Frobenius bimodule. In a separab le case\, a Frobenius bimodule and its dual form a Morita context. We also found that the category 2Cob2o-c of two coloured open surfaces is the free monoidal category on a bimodule btween two Cardy pairs. We moved then to th e category 2Cobd of surfaces with defect of codimension 1. We gave a dicrib tion of Cardy correspondences in this category and ended up with a conjectu re stating that the category 2Cobd is free on a Cardy correspondence in a s eparable case\, i.e. all Frobenius algebras are separable. We gave an examp le of a 2 dimensional topological field theory which we call a set-theoreti c 2 dimensional topological field theory. The target of this functor is the category of correspondences Corr. We showed that any Frobenius monoid in C orr is a multi-fusion ring. DTEND:20220301T163000Z DTSTAMP:20241114T071141Z DTSTART:20220301T153000Z LOCATION: SEQUENCE:0 SUMMARY:Mathematics Ph.D. candidate Mohmmad Zailai defends his dissertation \, March 1 UID:tag:localist.com\,2008:EventInstance_39297281459476 URL:https://calendar.ohio.edu/event/mathematics_phd_candidate_mohmmad_zaila i_defends_his_dissertation_march_1 END:VEVENT END:VCALENDAR