Speaker: Yidun Wan
Abstract: In this talk, we’ll develop a systematic framework for understanding symmetries in topological phases in 2 + 1 dimensions using the string-net model, encompassing both gauge symmetries that preserve anyon species and global symmetries permuting anyon species, including both invertible symmetries describable by groups and noninvertible symmetries described by categories. As an archetypal example, we reveal the first noninvertible categorical gauge symmetry of topological orders in 2 + 1 dimensions: the Fibonacci gauge symmetry of the doubled Fibonacci topological order, described by the Fibonacci fusion 2-category. Our approach involves two steps: first, establishing duality between different string-net models with Morita equivalent input fusion categories that describe the same topological order; and second, constructing symmetry transformations within the same string-net model when the dual models have isomorphic input fusion categories, achieved by composing duality maps with isomorphisms of degrees of freedom between the dual models. If time permits, I will also talk about a subsequent work on anyon condensation.
Time: Friday 13th December 2024, 10:30h-11:30h.
Location: Room 1410, SIMIS, Block A, No. 657 Songhu Road, Yangpu District, Shanghai
Send comments or questions to: Miguel Tierz (Seminar organizer; tierz at simis.cn) or to Jean-Emile Bourgine (Speaker’s host; bourgine at simis.cn)
Biography of the speaker: Yidun Wan is a tenured professor of physics at Fudan University. He has a diverse educational background, with bachelor degrees in computer science and economics from South China University of Technology (1998), master of computer science from University of Pennsylvania (2002), master of physics from University of Ottawa (2004), and PhD in theoretical physics from University of Waterloo and Perimeter Institute for Theoretical Physics (2009). He also did postdoctoral research at Kinki University, Tokyo University, and Perimeter Institute for Theoretical Physics from 2009 to 2016. He joined Fudan as a professor in 2016. His research interests include cosmology, topological orders, quantum information and computation, quantum gravity, and their interdisciplinary studies.
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