KenjiFukaya is a Japanese mathematician. His early work field was Riemannian geometry, especially the results related to the collapse of Riemannian manifold. Since then, his research direction is mainly symplectic geometry, especially the introduction and development of the so-called deep valley category theory. From April, 2065438 to April, 2003, Kloc-0, he joined the Simons Center for Geometry and Physics and served as a tenured professor at Stony Brook University.

Chinese name: Kenji Noguchi

Mbth: KenjiFukaya

Nationality: Japan

Date of birth:1March 959 12.

Occupation: mathematician (direction: symplectic geometry, gauge theory, Riemannian geometry)

Graduate school: Tokyo University (198 1 bachelor, 1986 doctor)

Main achievements: 1989 Geometric Atlas of Japan Mathematical Society.

Japan Mathematical Society Spring Award

Japan Bachelor's College Award in 2003

In 2009, he was elected as an academician of Japan Bachelor's College.

Masterpieces: Morse Homotopy, Infinite Category and Flohr Homology; Flower's lagrange intersection theory-anomalies and obstacles.

Kenji Noguchi completed his undergraduate and doctoral studies in the Department of Mathematics of the University of Tokyo. He received his bachelor's degree at 198 1 and his doctorate at 1986. 1983- 1990, assistant researcher and associate professor, University of Tokyo. 1994 went to Kyoto university as a full professor. In 20 13, he came to the United States and joined the Simons Center for Geometry and Physics in Brook, Si Tong.

Kenji Noguchi won the geometric Prize of the Japanese Mathematical Society in 1989 and the SpringPrize in 1994. He also won the Nobel Prize in Science in 2002, the Japanese Academic Award in 2003, the Japanese Science Award in 2009 and the Fujiwara Award in 20 12.

Kenji Noguchi's early work was in the field of Riemannian geometry, especially the result related to the collapse of Riemannian manifold. 1990, Noguchi was invited to give a speech at the International Congress of Mathematicians, entitled "The Collapse of Riemannian Manifolds and Its Application".

Then Abisa turned to symplectic geometry. Fukaya category is an important and active research field in symplectic geometry. It is an A- infinite category which is given a symplectic manifold, takes all its Lagrangian submanifolds as objects, and takes cohomology groups on Lagrangian Flohr as morphisms. It is named after the deep valley. This field is closely related to the homology of Flohr. Kontsevich's conjecture of homology mirror symmetry is based on deep valley work: this abstruse conjecture can be described as that the derived category of condensed layer on Keller manifold should be isomorphic to the deep valley category of "mirror" symplectic manifold.

Other contributions of Hasegawa Kenji to symplectic geometry include the proof of a version of Proof conjecture given by him in cooperation with KaoruOno. He also made many other contributions to mathematics, including important theorems about the collapse of Riemannian manifolds and topics related to physics, such as gauge theory and mirror symmetry. See the interview with Kenji Deep Valley for details.