BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Aaron Lauda (University of Southern California) DTSTART:20250813T160000Z DTEND:20250813T170000Z DTSTAMP:20260423T005843Z UID:TQFT/144 DESCRIPTION:Title: N onsemisimple Topological Quantum Computation\nby Aaron Lauda (Universi ty of Southern California) as part of Topological Quantum Field Theory Clu b (IST\, Lisbon)\n\n\nAbstract\nSince the foundational work of Freedman\, Kitaev\, Larsen\, and Wang\, it has been understood that 3-dimensional top ological quantum field theories (TQFTs)\, described via modular tensor cat egories\, provide a universal model for fault-tolerant topological quantum computation. These TQFTs\, derived from quantum groups at roots of unity\ , achieve modularity by semisimplifying their representation categories— discarding objects with quantum trace zero. The resulting semisimple categ ories describe anyons whose braiding enables robust quantum computation.\n \nThis talk explores recent advances in low-dimensional topology\, focusin g on the use of nonsemisimple categories that retain quantum trace zero ob jects to construct new TQFTs. These nonsemisimple TQFTs surpass their semi simple counterparts\, distinguishing topological features inaccessible to the latter. For physical applications\, unitarity is essential\, ensuring Hom spaces form Hilbert spaces. We present joint work with Nathan Geer\, B ertrand Patureau-Mirand\, and Joshua Sussan\, where nonsemisimple TQFTs ar e equipped with a Hermitian structure. This framework introduces Hilbert s paces with possibly indefinite metrics\, presenting new challenges.\n\nWe further discuss collaborative work with Sung Kim\, Filippo Iulianelli\, an d Sussan\, demonstrating that nonsemisimple TQFTs enable universal quantum computation at roots of unity where semisimple theories fail. Specificall y\, we show how Ising anyons within this framework achieve universality th rough braiding alone. The resulting braiding operations are deeply connect ed to the Lawrence–Krammer–Bigelow representations\, with the Hermitia n structure providing a nondegenerate inner product grounded in quantum al gebra.\n LOCATION:https://researchseminars.org/talk/TQFT/144/ END:VEVENT END:VCALENDAR