Entry Information
Shuanghe Fan
Dr
Male

15/07/1994
China
Passport
ED488
Chinese
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+8613126762875
北京市海淀区月泉路八家嘉园22号楼2单元1903
北京
China
Prof_Shing_Tung_YAU
Mathematical Sciences
N/A
My research focuses on advancing singularity theory and complex geometry through novel frameworks like higher-order Jacobian and Hessian matrices. Under the guidance of Prof. Yau and Zuo, I developed the higher-order Jacobian matrix theory, constructing new invariants that generalize classical Tjurina and Milnor algebras. Additionally, I pioneered the higher-order Hessian matrix theory to study projective equivalence of Calabi-Yau manifolds. By deriving determinant-based invariants, I completely distinguished non-equivalent families of K3 surfaces in ℂℙ³, addressing a decades-old problem. These contributions deepen the interplay between algebraic geometry and singularity theory.
Beyond research, I serve as Head of the Graduate Affairs Group of the Qiuzhen College, where I coordinate academic programs and foster collaboration among mathematics graduate students. This role has honed my ability to bridge theoretical innovation with practical academic leadership, ensuring that complex ideas translate into collaborative, real-world solutions.
I seek to join the Hong Kong Laureate Forum to engage with leading mathematicians, discuss extending these theories to other branches of mathematics, and explore applications in theoretical physics and computer science. My goal is to leverage both my research expertise and leadership experience to cultivate interdisciplinary collaborations that bridge abstract mathematics and concrete challenges across disciplines.
Postdoc
Singularity theory, Mathematics
Tsinghua University
Beijing


Beijing Institute of Mathematical Sciences and Applications (BIMSA)

Tsinghua University

First Academic or Research Referee *
Prof. Stephen Yau
Beijing Institute of Mathematical Sciences and Applications (BIMSA)
BIMSA Professor
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Second Academic or Research Referee
Prof. Huaiqing Zuo
Tsinghua University
Deputy Director of the Department of Mathematical Sciences, Tsinghua University
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Developed higher-order Jacobian theory, resolving singularity invariant conjectures via higher Nash blow-ups and extending Tjurina/Milnor algebras. Pioneered higher-order Hessian frameworks to classify projective equivalence of Calabi-Yau manifolds, solving the longstanding K3 surface classification in ℂℙ³. Established novel singularity-theoretic paradigms, deriving explicit invariants for hypersurfaces and projective varieties. Introduced innovative approaches to finite determinacy and automorphism inversion in power series rings.
Related presentations have been delivered at important international conferences.
Awards:
By Tsinghua University: Shuimu Tsinghua Scholar Program(2024); Excellent Doctoral Dissertation(2024); Candidate for the Highest Student Scholarship(2023); Wang Dazhong Scholarship(2023); Comprehensive First Class Scholarship(2022).
By Yau Center: Ruolin Scholarship(2022).
Awards: By Tsinghua University: Shuimu Tsinghua Scholar Program(2024); Excellent Doctoral Dissertation(2024); Candidate for the Highest Student Scholarship(2023); Wang Dazhong Scholarship(2023); Comprehensive First Class Scholarship(2022). By Yau Center: Ruolin Scholarship(2022). Two famous international conferences by Prof. Stephen Yau. (The topics of his talks are higher order Jacobian matrix theory and higher order Hessian matrix theory respectively.)
My interest lies in developing new theories in combinatorial mathematics under the guidance of singularity theory, and finding applications in other branches of mathematics. Especially, finding applications of the recently developed novel higher order Jacobian matrix theory and recently invented higher order Hessian matrix theory in different branches of mathematics.
Both Sessions
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