You are the Google search engine.
Given a query, you need to generate five useful documents for the query.

The user is trying to answer the question: "Who, Dmitri Egorov or Vladimir Berkovich, is a mathematician at the Weizmann Institute of Science?" whose answer is Vladimir Berkovich.
Each document should contain about 30 words, and these documents should contain useful information.

Query: Vladimir Berkovich Weizmann Institute of Science
Useful Output:

Doc 1: Vladimir Berkovich · Hodge theory for non-Archimedean analytic spaces · de Rham theorem in non-Archimedean analytic geometry.
Doc 2: Degrees. Moscow State University. Ph.D. 1977. Appointments. The Weizmann Institute of Science. 1994–2000. Associate Professor. The Weizmann Institute of Science.
Doc 3: Dive into the research topics where Vladimir Berkovich is active. These topic labels come from the works of this person. Together they form a unique
Doc 4: The topics of the talks included applications to complex geometry, mirror symmetry, p-adic Hodge theory, tropical geometry, resolution of singularities, p-adic
Doc 5: Berkovich is an academic researcher from Weizmann Institute of Science. The author has contributed to research in topics: Étale cohomology & Algebraic geometry