BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Marco De Renzi (University of Zurich) DTSTART:20230313T150000Z DTEND:20230313T160000Z DTSTAMP:20260423T021109Z UID:EQuAL/9 DESCRIPTION:Title: Al gebraic presentation of cobordisms and quantum invariants in dimensions 3 and 4\nby Marco De Renzi (University of Zurich) as part of European Qu antum Algebra Lectures (EQuAL)\n\n\nAbstract\nThe category 2Cob of 2-dimen sional cobordisms is freely generated by a commutative Frobenius algebra: the circle. This yields a complete classification of 2-dimensional TQFTs ( Topological Quantum Field Theories). In this talk\, I will discuss some co nsequences of analogous algebraic presentations in dimensions 3 and 4\, du e to Bobtcheva and Piergallini. In both cases\, the fundamental algebraic structures are provided by certain Hopf algebras called BPH algebras. In d imension 3\, I will consider the category 3Cob of connected cobordisms bet ween connected surfaces with connected boundary. I will explain that an al gebraic presentation conjectured (or rather announced without proof) by Ha biro is in fact equivalent to the one established by Bobtcheva and Piergal lini. In dimension 4\, I will focus on a category denoted 4HB\, whose morp hisms are 2-deformation classes of 4-dimensional 2-handlebodies. I will sh ow that any unimodular ribbon category contains a BPH algebra\, which can be characterized very explicitly. This result proves the existence of a ve ry large family of TQFT functors on 4HB. Finally\, I will explain that a u nimodular ribbon category has the potential to detect exotic phenomena in dimension 4 only if it is neither semisimple nor factorizable. This is a j oint work with A. Beliakova\, I. Bobtcheva\, and R. Piergallini.\n LOCATION:https://researchseminars.org/talk/EQuAL/9/ END:VEVENT END:VCALENDAR