Beijing Institute of Mathematical Sciences and Applications Beijing Institute of Mathematical Sciences and Applications

  • About
    • President
    • Governance
    • Partner Institutions
    • Visit
  • People
    • Management
    • Faculty
    • Postdocs
    • Visiting Scholars
    • Staff
  • Research
    • Research Groups
    • Courses
    • Seminars
  • Join Us
    • Faculty
    • Postdocs
    • Students
  • Events
    • Conferences
    • Workshops
    • Forum
  • Life @ BIMSA
    • Accommodation
    • Transportation
    • Facilities
    • Tour
  • News
    • News
    • Announcement
    • Downloads
About
President
Governance
Partner Institutions
Visit
People
Management
Faculty
Postdocs
Visiting Scholars
Staff
Research
Research Groups
Courses
Seminars
Join Us
Faculty
Postdocs
Students
Events
Conferences
Workshops
Forum
Life @ BIMSA
Accommodation
Transportation
Facilities
Tour
News
News
Announcement
Downloads
Qiuzhen College, Tsinghua University
Yau Mathematical Sciences Center, Tsinghua University (YMSC)
Tsinghua Sanya International  Mathematics Forum (TSIMF)
Shanghai Institute for Mathematics and  Interdisciplinary Sciences (SIMIS)
BIMSA > Algebraic Topology and its Applications
Algebraic Topology and its Applications

Research Group

  • Algebraic Geometry
  • Algebraic Topology and its Applications
  • Analysis and Geometry
  • Artificial Intelligence and Machine Learning
  • Computational Mathematics
  • Digital Economy
  • General Relativity and Partial Differential Equations
  • Mathematical Physics
  • Number Theory and Representation Theory
  • Quantum Fields and Strings
  • Quantum Symmetry
  • Statistics, Probability and Data Science
Introduction
Algebraic topology is about the study of quantitative features of spaces that are independent of continuous deformations. It often studies the intricate relationships between continuous operations like pulling or stretching and properties pertaining to corresponding algebraic structures. It relies on central concepts of homotopy and homology. The abstraction and discretization of algebraic topology can be applied to the study of higher-order structures and dynamics of complex systems. The research area focuses on the following directions: 1) Fundamental research on all subjects in algebraic topology, 2) application-guided research developing topological foundations of higher-order interaction networks focusing on digraphs, mixture graphs, hyper(di-)graphs and hyper-networks related to GLMY homology and homotopy of digraphs introduced by Shing-Tung Yau, and introducing new topology theories in data, 3) practical applications of algebraic topology in data science and artificial intelligence focusing on testing the effectiveness of topological approaches developed at BIMSA.
Focus topics: 1) GLMY-theory and magnitude homology theory, 2) Non-commutative patterns in unstable homotopy theory, 3) Exponents of homotopy groups, 4) Decomposition of loop spaces, 5) Homotopy aspects of knot theory, 6) Topological foundations of complex networks, 7) AI methods in algebraic topology, 8) Combinatorial topology based data analysis, 9) Knot theory based data analysis, 10) Representations and calculus of functors.
The members in the group will work along one or more above-mentioned directions, with aiming to one or more of the focus topics via collaborative interactions among group members.
PI
Jie Wu

Jie Wu

Professor

Group Assistant
Yang Yang Ruan

Yang Yang Ruan

Postdoc

Faculty
Sergei Ivanov

Sergei Ivanov

Professor

Feng Chun Lei

Feng Chun Lei

Professor

Jing Yan Li

Jing Yan Li

Assistant Professor

Postdocs
Matthew Burfitt

Matthew Burfitt

Postdoc

Xin Fu

Xin Fu

Postdoc

Grigory Papayanov

Grigory Papayanov

Postdoc

Meng Meng Zhang

Meng Meng Zhang

Postdoc

Yun Peng Zi

Yun Peng Zi

Postdoc

Visitors

Bing Fang

Visiting Scholar

Xiang Liu

Xiang Liu

Visiting Scholar

Vassily Manturov

Visiting Scholar

Yury Muranov

Visiting Scholar

Student
Ran Liu

Ran Liu

PhD Candidate

Yubo Liu

Yubo Liu

PhD Candidate

Xiaoxi Wang

PhD Candidate

Jian Yao

Jian Yao

PhD Candidate

Hequn Zhang

Hequn Zhang

PhD Candidate

Beijing Institute of Mathematical Sciences and Applications
CONTACT

No. 544, Hefangkou Village Huaibei Town, Huairou District Beijing 101408

北京市怀柔区 河防口村544号
北京雁栖湖应用数学研究院 101408

Tel. 010-60661855
Email. administration@bimsa.cn

Copyright © Beijing Institute of Mathematical Sciences and Applications

京ICP备2022029550号-1

京公网安备11011602001060 京公网安备11011602001060