BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Aaron Lauda (The University of Southern California) DTSTART:20250226T080000Z DTEND:20250226T093000Z DTSTAMP:20260422T161058Z UID:HKUST-AG/70 DESCRIPTION:Title: Nonsemisimple Topological Quantum Computation\nby Aaron Lauda (The U niversity of Southern California) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture held in Room 4472 (Lifts 25/26).\n\nAbstract\nSince the foundational work of Freedman\, Kitaev\, Larsen\, and Wang\, it has been understood that 3-dimensional topological quantum field theories (TQFTs)\, described via modular tensor categories\, provide a universal model for f ault-tolerant topological quantum computation. These TQFTs\, derived from quantum groups at roots of unity\, achieve modularity by semisimplifying t heir representation categories—discarding objects with quantum trace zer o. The resulting semisimple categories describe anyons whose braiding enab les robust quantum computation.\n\nThis talk explores recent advances in l ow-dimensional topology\, focusing on the use of nonsemisimple categories that retain quantum trace zero objects to construct new TQFTs. These nonse misimple TQFTs surpass their semisimple counterparts\, distinguishing topo logical features inaccessible to the latter. For physical applications\, u nitarity is essential\, ensuring Hom spaces form Hilbert spaces. We presen t joint work with Nathan Geer\, Bertrand Patureau-Mirand\, and Joshua Suss an\, where nonsemisimple TQFTs are equipped with a Hermitian structure. Th is framework introduces Hilbert spaces with possibly indefinite metrics\, presenting new challenges.\n\nWe further discuss collaborative work with S ung Kim\, Filippo Iulianelli\, and Sussan\, demonstrating that nonsemisimp le TQFTs enable universal quantum computation at roots of unity where semi simple theories fail. Specifically\, we show how Ising anyons within this framework achieve universality through braiding alone. The resulting braid ing operations are deeply connected to the Lawrence-Krammer-Bigelow repres entations\, with the Hermitian structure providing a nondegenerate inner p roduct grounded in quantum algebra.\n LOCATION:https://researchseminars.org/talk/HKUST-AG/70/ END:VEVENT END:VCALENDAR