BEGIN:VCALENDAR VERSION:2.0 CALSCALE:GREGORIAN PRODID:iCalendar-Ruby BEGIN:VEVENT CATEGORIES:Lectures & Presentations DESCRIPTION:Mathematics Ph.D. candidate Kevin Pomorski defends his disserta tion on "On Braided Monoidal 2-Categories" on March 3 at 5 p.m. via Teams.\ n\n \n\nJoin on Teams. \n\nThe dissertation committee is Alexei Davydov\, M arcel Bischoff\, Sergio Lopez-Permouth\, and Nancy Sandler.\n\n\n\nAbstract : In Topological Field Theories (TFTs)\, there is a well documented correla tion between 3-dimensional TFTs and braided monoidal categories. While brai ded monoidal 2-categories have been expected to have applications to 4-dime nsional TFTs\, there are very few known examples of braided monoidal 2-cate gories. The major goal of this dissertation is to present a categorificatio n of a result of Pareigis. Namely\, that modules over a commutative algebra in a braided monoidal category form a braided monoidal category. The categ orified statement is that pseudomodules over a braided pseudomonoid in a br aided monoidal 2-category form a braided monoidal 2-category. This result w ould be an example of constructing braided monoidal 2-categories from exist ing braided monoidal 2-categories. We approach this by constructing a new l anguage which simplifies some of the complexities coming from relative tens or products of pseudomodules. The relationships between monoidal categories and multicategories has been well documented e.g. by Leinster. We define t he notion of a multi-2-category\, as well as the notion of a braided multi- 2-category. We then construct braided pseudomonoids in braided multi-2-cate gories and examine pseudomodules over them. The main theorem of the dissert ation is that local pseudomodules over a braided pseudomonoid in a braided multi-2-category forms a braided multi-2-category. A second result is a rev ision to the Joyal-Street definition of a balanced 2-category. We give a co herence for balanced 2-categories which was omitted in the original definit ion. DTEND:20220303T230000Z DTSTAMP:20240921T094732Z DTSTART:20220303T220000Z LOCATION: SEQUENCE:0 SUMMARY:Mathematics Ph.D. candidate Kevin Pomorski defends his dissertation \, March 3 UID:tag:localist.com\,2008:EventInstance_39297321114861 URL:https://calendar.ohio.edu/event/mathematics_phd_candidate_kevin_pomorsk i_defends_his_dissertation_march_3 END:VEVENT END:VCALENDAR