Recently, Associate Professor Guo Shuai and collaborators in the School of Mathematical Sciences of Peking University have made an important breakthrough in the A-model structure of BCOV theory. His paper "Polynomial Structure of Gromov–Witten Potential of Quintic3-folds" was accepted by Annals of Mathematics, a leading international mathematical journal.
Screenshot of the Math Yearbook website
Mirror symmetry is a cutting-edge branch of the rise of modern mathematical physics in the past two or three decades, and its earliest derivation from string duality in physics. Mathematically , it predicts the counting problem of rational curves ( deficit 0 ) in Three-dimensional Manifolds of Calabi-Yau ( Gromov-Witten invariants ) , and the periodic integrals on their mirrored manifolds can be established by such a magical bridge as mirror mapping. When the curve to be counted is greater than 0, the mathematical statement of mirror symmetry is always unclear. In the 1990s, four prominent physicists, the Bershadsky-Cecotti-Ooguri-Vafa system, studied the mirror symmetry theory of high-deficit lattice, and they discovered a series of mathematical structures that must be satisfied with the high-deficit theory by using the Feynman path integral of type II B topological strings. These structures indicate that high deficit potential functions should have some finite generation properties, as well as controllable initial conditions. For the typical Calaby-Yau three-dimensional manifold of a five-dimensional hypersurface, Yamaguchi-Yau gives a more precise mathematical description based on BCOV theory, which is called the polynomial structure conjecture. Associate Professor Guo Shuai of the School of Mathematical Sciences of Peking University, in collaboration with Professor Li Jun of the Shanghai Center for Mathematics of Fudan University, and Professor Huailiang Zhang of the Hong Kong University of Science and Technology, used NMSP theory to mathematically achieve the finite generative properties and finite initial conditions of the BCOV conjecture on five-dimensional hypersurfaces, and thus proved the Yamaguchi-Yau polynomial structure conjecture. Academician Tian Gang, a well-known expert in the field, said: This paper solves a well-known problem in the field of counting geometry, and many internationally renowned mathematicians have studied it for a long time, and there has been no substantial progress. Guo Shuai has played a key role in solving these difficult problems.
Guo Shuai
Shuai Guo received his bachelor's degree from Tsinghua University in 2006, visited Princeton University in the United States for one year with the joint doctoral program of the China Scholarship Council in 2010, and received his Ph.D. from Tsinghua University in 2011. In 2011, he was funded by the Simons Foundation to start postdoctoral research at the Beijing International Center for Mathematical Research at Peking University, joined the School of Mathematics of Peking University in 2013, and became an associate professor in 2016, winning the 2019 Qiushi Outstanding Young Scholar Award.