Zhenghan Wang (Chinese: 王正汉; born April 26, 1965) is a Chinese-American mathematician and principal researcher at Microsoft Station Q, as well as a professor of mathematics at the University of California, Santa Barbara. He is known for his contributions to topological quantum computing, low-dimensional topology, and the mathematical theory of topological phases of matter.
Education and Career
Wang was born in Tsingtao, China. He earned a B.S. and M.S. in mathematics from the University of Science and Technology of China in 1989, and a Ph.D. in mathematics from the University of California, San Diego in 1993 under the supervision of Michael Freedman. His doctoral dissertation was titled The Classification of Topological Four-Manifolds with Infinite Cyclic Fundamental Group.
He served as an assistant professor at the University of Michigan from 1993 to 1996, and was a faculty member at Indiana University Bloomington from 1996 to 2007. In 2005, he joined Microsoft Station Q in Santa Barbara as a senior researcher. He became a full professor of mathematics at UC Santa Barbara in 2012 (currently on indefinite leave) and served as a Distinguished Visiting Research Chair at the Perimeter Institute for Theoretical Physics from 2013 to 2020.
Research Contributions
Topological Quantum Computing
Wang made foundational contributions to topological quantum computation. In a series of papers with Michael Freedman, Michael J. Larsen, and Alexei Kitaev, he established the abstract equivalence of topological quantum computation with the standard quantum circuit model. This work showed that Fibonacci anyon models can be used to build a universal quantum computer.
Algebraic Theory of Topological Phases
Wang has contributed extensively to the formal algebraic theory of two-dimensional topological quantum phases, including work on the structure and classification of bosonic topological order (modular tensor categories), fermionic topological order (super-modular tensor categories), and symmetry-enriched topological order (G-crossed modular tensor categories). Notable results include the rank-finiteness theorem for modular categories (with Bruillard, Ng, and Rowell) and the classification of super-modular categories.
Walker-Wang Model
Along with Kevin Walker, Wang introduced the Walker-Wang model, a three-dimensional topological quantum field theory that has been used to describe the boundaries of topological insulators and to construct nontrivial quantum cellular automata.
Topology of 4-Manifolds
Earlier in his career, Wang specialized in the topology of 4-manifolds, including work on the classification of nonorientable 4-manifolds with infinite cyclic fundamental group.
Awards and Recognition
Wang was included in the 2019 class of Fellows of the American Mathematical Society. He is the author of the book Topological Quantum Computation (CBMS Regional Conference Series in Mathematics, vol. 112, AMS, 2010).
Personal Life
Wang has been married to Dr. Yanyun Chen since 1993. They have two children.
