Prof. Guozhen Wang, jointly with Ruochuan Liu, has online published a research paper by Inventiones Mathematicae. This is the eleventh research paper authored by researchers in Shanghai Center for Mathematical Sciences that has published in one of the top-four international mathematical journals.
The paper is “Topological cyclic homology of local fields” (https://link.springer.com/article/10.1007/s00222-022-01134-9#article-info).
Topological cyclic homology is an extension of the cyclic homology developed by Connes (1983 Fields Medal winner) and introduced in the 1990s by Bokstedt - Hsiang- Madsen. The work of Dundas -- Goodwillie -- McCarthy makes topological cyclic homology an important tool in algebraic K-theory computations. In 2003, Hesselholt-Madsen first computed the topological cyclic homology of p-adic local fields for all odd primes p
More recently, work by Bhatt-Morrow-Scholze has shed new light on the theory of topological cyclic homology and p-adic cohomology -- in particular prismatic cohomologyintroduced by Bhatt (2022 ICM one-hour Presenter）, and Scholze (2018 Fields Medal winner). This makes the study of topological cyclic homology also important in arithmetic geometry.
Influenced by these works, Ruochuan Liu and Guozhen Wang jointly studied topological cyclic homology and proposed a new method to calculate topological cyclic homology, called descent spectral sequence method. By using the descent spectral sequence method, they greatly simplify the computations of topological cyclic homology for p-adic local fields and solve the remaining p =2 case. In addition, the theoretical framework of the descent spectral sequence method also provides a formulation of the cohomology of prisms based on a Stacky reformulation.
Prof. Wang received his bachelor's and master's degrees from Peking University, in 2008 to 2011; received his Ph.D. from MIT in 2015. After, he became a postdoctoral fellow at the University of Copenhagen. In 2017, Prof. Wang joined SCMS as a postdoctoral fellow. Shortly after, he became a young researcher. In 2020, he had been an associate professor. Since 2022, he has been promoted as a professor at SCMS.