Condensed matter physics, in particular topological orders.
Mathematics for quantum field theory and condensed matter physics, in particular higher category theory, Hopf algebras and operator algebras.
Education
Bachelor of Science, Department of Physics, Peking University (2019).
Master of Science, Shenzhen Institute of Quantum Science and Engineering, Southern University of Science and Technology (2024).
Thesis: Local Operator Algebras in Levin-Wen Models Form a Weak Hopf Cocategory. Advisor: Liang Kong.
Abstract: Weak Hopf algebras (WHAs) have wide applications in the studies of quantum field theory, subfactor and topological order. One of the basic theorem of WHAs, the Reconstruction theorem (due to T. Hayashi), states that one can obtain a WHA from each pair (C,F:C->BiMod(R)), where C is a finite tensor category, F is a tensor functor and R is a separable algebra; Conversely, each WHA gives rise to such a pair. The appearance of R or BiMod(R) may seem ad hoc to many; In this talk I interpret this theorem as a special case of 2-categorical theorem, where R or BiMod(R) do not explicitly appear. This is based on a joint work with Zhi-Hao Zhang on understanding the algebraic structures in Kitaev-Kong (2012).
Abstract: The center of an algebra is the subalgebra consisting of elements commuting with every element of this algebra. It has a universal property identified by Lurie (2009) which can be easily generalized to various set-ups. In this talk we announce a verification that the Drinfeld double construction of a finite dimensional Hopf algebra gives rise to the 2-categorical center of this Hopf algebra.
Abstract: Higher dimensional or categorical algebras and their higher representations are recently widely used in the study of topological orders. In this expository talk I introduce the geometric intuitions behind those applications, present a periodic table of those higher algebras, and introduce J. Lurie's notion of center of higher algebras which is fundamental for understanding their higher representations. If time permits, I will also talk about how to apply center to topological orders. The higher algebras appearing in this talk are conjecturally special cases of En-algebras whose definition is given by Lurie based on the work of May, Boardman-Vogt, Dunn and others.
Talk: A Universal Property of the Drinfeld Double of Finite Dimensional Hopf Algebras. Jan 26, 2024.
Advances in Quantum Algebra.
(slides)
Abstract: The center of an algebra has a universal property identified by Lurie which can be easily generalized to any object in a category with a monoidal structure. Hopf algebras live naturally in a monoidal 2-category by the observation of Street and McCrudden, and we show that the center of a finite dimensional Hopf algebra coincides with the Drinfeld double construction.
Academic Services
Co-organizer of Shenzhen School on Topological Orders and Category Theory (拓扑序与范畴学讲习会)
(link), which lasts 7 days. Mar 18-24, 2023. Shenzhen, China. Other co-organizers:
Chunyu Bai,
Gang Chen,
Liang Kong, Holiverse Yang and
Zhi-Hao Zhang.