BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sean Sanford (Ohio State University) DTSTART:20250409T150000Z DTEND:20250409T163000Z DTSTAMP:20260422T174244Z UID:tandg/30 DESCRIPTION:Title: M anifestly unitary higher Hilbert spaces\nby Sean Sanford (Ohio State U niversity) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\n Abstract\nA key aspect of quantum theory its insistence that states evolve via unitary transformations. In order to understand the symmetries of hig her dimensional quantum field theory\, we need to develop higher dimension al analogues of unitarity. The language and theory of higher categories ha s greatly clarified the way we express these higher symmetries\, but unfor tunately this language imposes a certain dogma seems to be in conflict wit h various attempts at describing unitarity. In the nLab for example\, ther e is a great debate over whether or not unitary structures on a (higher) c ategory are `evil’\; at term which is both dogmatic and technically prec ise.\n\nVarious attempts have been made to force these structures to `play nice’ with one another\, to varying degrees of success. In this talk I will present our most recent contribution to these efforts: defining the n otion of a 3-Hilbert space. Our work aims to encode a kind of evaluation o n spheres of every dimension that plays nicely with duality structures tha t are imposed by the cobordism hypothesis. I will show how this compatibil ity is stronger than simply having daggers at all levels\, thus differenti ating our construction from previous attempts at higher unitarity. If time permits\, we will discuss a roadmap for unitarity in any dimension via a unitary version of condensation completion.\n LOCATION:https://researchseminars.org/talk/tandg/30/ END:VEVENT END:VCALENDAR