代数及几何工具在计算数学中的应用，包括张量计算，流形计算，计算复杂度，数值线性代数。

2007-09--2012-08   Texas A&M University   博士
2003-09--2007-08   四川大学   学士学位

2017--至今, 中科院数学与系统科学研究院，副研究员
2015--2017, University of Chicago, 博士后
2012--2015, University of Chicago, L. E. Dickson Instructor

2023--至今, SIAM Journal on Applied Algebra and Geometry, Associate Editor

   

1. (with Z. Dai and L.-H Lim) Complex matrix inversion via real matrix inversions, Numerische Mathematik, 2024, 156, pp. 2179-2219. (arXiv). 
2. (with Q. Y. Chen and J. Uhlmann) Generalizing Frobenius inversion to quaternion matrices, Numerical Algorithms, 2024, 97, pp. 101-116. (arXiv)   
3. (with J. T. Yang and L. H. Zhi) Computing sparse Fourier sum of squares on finite abelian groups in quasi-linear time, Applied and Computational Harmonic Analysis, 2024, 73, pp. 101686. (arXiv)  
4. (with Q. L. Huang and X. S. Gao) Skew-sparse matrix multiplication, Journal of Symbolic Computation, 2024, 121, pp. 102240. (arXiv)  
5. (with S. L. Hu) Linear convergence of an alternating polar decomposition method for low rank orthogonal tensor approximations, Mathematical Programming (Series A), 2023, 199, pp. 1305-1364. (arXiv)
6. (with S. W. Wong and L.-H. Lim) Optimization on flag manifolds, Mathematical Programming (Series A),  2022, 194(1-2), pp. 621-660. (arXiv)
7. (with L.-H. Lim and S. W. Wong) The Grassmannian of affine subspaces, Foundations of Computational Mathematics, 2021, 21, pp. 537-574. (arXiv)
8. (with P. Comom, L.-H. Lim and Y. Qi) Topology of tensor ranks, Advances in Mathematics, 2020, 367, pp. 107128. (arXiv)
9. (with L.-H. Lim, S. W. Wong) Numerical Algorithms on the Affine Grassmannian, SIAM Journal on Matrix Analysis and Applications, 2019, 40(2), pp. 371-393. (arXiv)
10. (with J. W. Nie) Hankel tensor decompositions and ranks, SIAM Journal on Matrix Analysis and Applications, 2019, 40(2), pp. 486-516. (arXiv) 
11. (with L.-H. Lim and R. Sepulchre) Geometric distance between positive definite matrices of different dimensions, IEEE Transactions on Information Theory, 2019, 65(9), pp. 5401-5405. (arXiv) 
12. (with L.-H. Lim) Fast structured matrix computations: tensor rank and Cohn-Umans method, Foundations of Computational Mathematics, 2018, 18(1), 45-95. (arXiv)
13. (with S. L. Hu) Inverse eigenvalue problems for tensors, Communications in Mathematical Sciences, 2017, 15(6), pp. 1627-1649. (arXiv) 
14. (with L.-H. Lim) Cohomology of cryo-electron microscopy, SIAM Journal on Applied Geometry and Algebra, 2017, 1(1), pp. 507-535. (arXiv)
15. New classes of matrix decompositions, Linear Algebra and its Applications, 2017, 514, pp. 47-81. (arXiv)
16. (with L.-H. Lim) Schubert varieties and distances between linear spaces of different dimensions, SIAM Journal on Matrix Analysis and Applications, 2016, 37(3), pp. 1176-1197. (arXiv)  
17. (with S. L. Hu) Multiplicities of tensor eigenvalues, Communications in Mathematical Sciences, 2016, 14(4), pp. 1049-1071. (arXiv)
18. (with L.-H. Lim) Every matrix is a product of Toeplitz matrices, Foundations of Computational Mathematics, 2016, 16(3), pp. 577-598. (arXiv)
19. (with J. M. Landsberg and Y. Qi) On the geometry of tensor network states, Quantum Information & Computation, 2012, 12(3-4), pp. 346-354. (arXiv)
20. The stabilizers of immanants, Linear Algebra and Its Applications, 2011, 435(5), pp. 1085-1098. (arXiv)

1. (with Q. Y. Chen) A quasi-optimal lower bound for skew polynomial multiplication, In Proceedings of the 49th International Symposium on Symbolic and Algebraic Computation (ISSAC '24), pp. 74-81. (arXiv) [Distinguished Student Author Award]
2. (with J. T. Yang and L. H. Zhi) Lower bounds of functions on finite abelian groups, In: Wu, W., Tong, G. (eds) Computing and Combinatorics. COCOON 2023. Lecture Notes in Computer Science, vol 14423.
3. (with L.-H. Lim) Ubiquity of the exponent of matrix multiplication, In Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation (ISSAC '20), pp. 8-11.
4. (with Y. Qi, P. Comon and L.-H. Lim) Path connectedness of tensor ranks, 27th European Signal Processing Conference (EUSIPCO 2019), pp. 1-5.
5. (with L.-H. Lim) Algorithms for structured matrix-vector product of optimal bilinear complexity, 2016 IEEE Information Theory Workshop (ITW 2016), pp. 310-314.  

1. (with L. X. Wang) An estimate for positive definite functions on finite abelian groups and its applications, 2025, submitted. (arXiv) 
2. (with S. L. Hu) Generic linear convergence for algorithms of non-linear least squares over smooth varieties, 2025, submitted. (arXiv)
3. (with Z. H. Lai and L.-H. Lim) Euclidean distance degree in manifold optimization, 2025, submitted. (arXiv)
4. (with J. Y. Lu) The Cayley Transform on Representations, 2025, submitted. (arXiv)
5. (with L.-H. Lim and X. Lu) Special orthogonal, special unitary, and symplectic groups as products of Grassmannians, 2025, submitted. (arXiv)
6. (with Q. Y. Chen) Stability of ranks under field extensions, 2024, submitted. (arXiv)
7. (with Z. H. Lai and L.-H. Lim) Grassmannian optimization is NP-hard, 2024, submitted. (arXiv)
8. (with Y. Wang) The sparseness of g-convex functions, 2024, submitted. (arXiv)
9. (with Z. H. Lai and L.-H. Lim) Simple matrix expressions for the curvatures of Grassmannian, 2024, submitted. (arXiv)
10. (with L.-H. Lim) Degree of the Grassmannian as an affine variety, 2024, submitted. (arXiv)
11. (with L.-H. Lim), Minimal equivariant embeddings of the Grassmannian and flag manifold, 2024, submitted. (arXiv)
12. (with Z. J. Li) Rational curves on real classical groups, 2024, submitted. (arXiv)
13. (with L.-H. Lim) Simple matrix models for the flag, Grassmann and Stiefel manifolds, 2024, submitted. (arXiv)
14. (with P. Liu) Bundle-based similarity measurement for positive semidefinite matrices, 2023. (arXiv)
15. (with S. L . Hu) When geometry meets optimization theory: partially orthogonal tensors, 2023. (arXiv)
16. (with J. T. Yang and L. H. Zhi) Fourier sum of squares certificates, 2023. (arXiv)
17. (with Z. H. Lai and L.-H. Lim) Simpler Grassmannian optimization, 2022. (arXiv)
18. (with M. Niu, P. Cheung, Z. W. Dai and Y. Liu) Intrinsic Gaussian processes on manifolds and their accelerations by symmetry, 2022. (arXiv)
19. (with Z. H. Lai and L.-H. Lim) Simpler flag optimization, 2022. (arXiv)
20. (with L.-H. Lim) Tensor network states ranks, 2021. (arXiv)
21. (with T. R. Gao and L.-H. Lim) Semi-Riemannian manifold optimization, 2019. (arXiv)
22. (with J. W. Nie and L. H. Zhi) Tensor decompositions on algebraic varieties, 2017. (arXiv)

• IMS-NTU joint workshop on Applied Geometry for Data Sciences, Singapore (2024) 
• SIAM Conference on Applied Linear Algebra, Sorbonne University, Paris, France (2024)
• Algebraic geometry and complexity theory workshop, Warsaw, Poland (2022)
• SIAM Conference on Applied Algebraic geometry, Texas A&M University, College Station, Texas, USA (2021)
• SIAM Conference on Applied Linear Algebra, New Orleans, Louisana, USA (2021)
• Data Science Seminar, Mathematical Institute, Orxford University, Oxford, UK (2021)

中国

中科院数学与系统科学研究院: 陆镜宇，李子佳，杨剑霆，支丽红，高小山

山东大学: 黄巧龙

国防科技大学: 胡胜龙

美国

University of Chicago: Lek-Heng Lim, Ken Sze-Wai Wong,  Tingran Gao, Zhen Dai, Xiang Lu

Texas A&M University: Joseph M. Landsberg

University of Berkeley at San Diego: Jiawang Nie

University of Missouri: Jeffrey Uhlmann

University of Texas at Austin: Zehua Lai

法国

CNRS: Pierre Comon

Ecole Polytechnique: Yang Qi 

英国

University of Glasgow: Mu Niu 

University of Cambridge: Rodolphe Sepulchre

• 华为敞口项目，基于流形的数据压缩和传输算法，72万, 课题负责人，2022--2023
• 国家重点研发计划，隐私保护数据处理的数学方法，课题组成员，2021--2025
• 华为敞口项目，通信中的结构矩阵乘法，64万, 课题负责人，2021--2022
• 中国科学院稳定支持基础研究领域青年团队，1500万，课题组成员，2021-2026
• 科技部重点专项，数据智能安全核心数学问题的高效算法及其应用，480万，课题组成员，2019--2021
• 国家自然科学基金青年项目，与子空间相关的流形上的数值微分几何， 26万, 课题负责人， 2019--2021
• 科技部重点专项，量子调控与量子信息重点， 200万，课题组成员，2018--2022
• 海外高层次人才引进计划青年项目（优先支持），300万，课题负责人，2018--2021

• 国际符号与代数计算会议（ISSAC）最佳学生论文，2024 
• 华为无线网络产品线优秀合作项目奖，2023 
• 吴文俊计算机数学青年学者奖，2023
• 华为技术合作成果转化二等奖，2022
• 中国科学院数学与系统科学研究院“陈景润未来之星”，2021
• 中国科学院数学与系统科学研究院系统所关肇直青年研究奖，2017

• 刘沿清（硕士）： 2023--至今
• 王立夏（博士）： 2022--至今（华罗庚奖学金，合作论文：1）
• 陈琦元（博士）： 2021--至今 （华罗庚奖学金，ISSAC '24最佳学生论文奖，合作论文：1, 2, 3)
• 王愚（博士）： 2020--至今（合作论文：1)
• 刘鹏（博士）：2018--2024（华为技术合作成果转化二等奖，华为无线网络产品线优秀合作项目奖，合作论文：1）