基本信息

叶科  男  博导  中国科学院数学与系统科学研究院
电子邮件： keyk@amss.ac.cn
通信地址： 中关村东路55号思源楼
邮政编码： 100190

​其他：googlesites, google scholar

研究领域

代数及几何工具在各个领域中的应用，包括张量计算，流形上的优化算法，多重线性系统的计算复杂度问题以及线性方程组的快速解法。

教育背景

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

工作经历


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

学术兼职

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

论文发表

   
已发表论文（期刊）

  1. (with Q. L. Huang and X. S. Gao) Skew-sparse matrix multiplication, Journal of Symbolic Computation, 2024, 121, pp. 102240. (arXiv)
  2. (with S. L. Hu) Linear convergence of an alternating polar decomposition method for low rank orthogonal tensor approximations, Mathemtical Programming (Series A), 2023, 199, pp. 1305-1364. (arXiv)pages
  3. (with S. W. Wong and L.-H. Lim) Optimization on flag manifolds, Mathematical Programming (Series A),  2022, 194(1-2), pp. 621-660. (arXiv)
  4. (with L.-H. Lim and S. W. Wong) The Grassmannian of affine subspaces, Foundations of Computational Mathematics, 2021, 21, pp. 537-574. (arXiv)
  5. (with P. Comom, L.-H. Lim and Y. Qi) Topology of tensor ranks, Advances in Mathematics, 2020, 367, pp. 107128. (arXiv)
  6. (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)
  7. (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)
  8. (with J. W. Nie) Hankel tensor decompositions and ranks, SIAM Journal on Matrix Analysis and Applications, 2019, 40(2), pp. 486-516. (arXiv)
  9. (with L.-H. Lim) Fast structured matrix computations: tensor rank and Cohn-Umans method, Foundations of Computational Mathematics, 2018, 18(1), 45--95. (arXiv)
  10. (with L.-H. Lim) Cohomology of cryo-electron microscopy, SIAM Journal on Applied Geometry and Algebra, 2017, 1(1), pp. 507-535. (arXiv)
  11. (with S. L. Hu) Inverse eigenvalue problems for tensors, Communications in Mathematical Sciences, 2017, 15(6), pp. 1627-1649. (arXiv)
  12. New classes of matrix decompositions, Linear Algebra and its Applications, 2017, 514, pp. 47-81. (arXiv)
  13. (with L.-H. Lim) Every matrix is a product of Toeplitzmatrices, Foundations of Computational Mathematics, 2016, 16(3), pp. 577-598. (arXiv)
  14. (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)
  15. (with S. L. Hu) Multiplicities of tensor eigenvalues, Communications in Mathematical Sciences, 2016, 14(4), pp. 1049-1071. (arXiv)
  16. (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)
  17. The stabilizers of immanants, Linear Algebra and Its Applications, 2011, 435(5), pp. 1085-1098. (arXiv)

已发表论文（会议）

  1. (with J. T. Yang and L. H. Zhi) Lower bounds of functions on finite abelian groups, The 29th International Computing and Combinatorics Conference (COCOON 2023), accepted.
  2. (with L.-H. Lim) Ubiquity of the exponent of matrix multipication, Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation (ISSAC'20), pp. 8-11.
  3. (with Y. Qi, P. Comon and L.-H. Lim) Path connectedness of tensor ranks, 27th European Signal Processing Conference (EUSIPCO 2019), pp. 1-5.
  4. (with L.-H. Lim) Algorithms for structured matrix-vector product of optimal bilinear complexity, 2016 IEEE Information Theory Workshop (ITW), pp. 310-314.

预印本

    1. (with J. T. Yang and L. H. Zhi) Short certificates for MAX-SAT via Fourier sum of squares, 2023, submitted. (arXiv)

    2. (with Q. Y. Chen and J. Uhlmann) Generalizing Frobenius inversion to quaternion matrices, 2023, submitted. (arXiv) 

    3. (with S. L . Hu) When geometry meets optimization theory: partially orthogonal tensors, 2022, submitted. (arXiv)

    4. (with Z. H. Lai and  L.-H. Lim) Simpler flag optimization, 2022, in progress. (arXiv)

    5. (with Z. Dai and L.-H Lim) Inverting a complex matrix, 2022, in progress. (arXiv) 

    6. (with Z. H. Lai and  L.-H. Lim) Simpler Grassmannian optimization, 2022, in progress. (arXiv)

    7. (with J. T. Yang and L. H. Zhi) Computing sparse Fourier sum of squares on finite abelian groups in quasi-linear time, 2022, in progress. (arXiv) 

    8. (with L.-H. Lim) Tensor network states ranks, 2021, in progress. (arXiv)

    9. (with M. Niu and P. Cheung) Heat kernel and intrinsic Gaussian processes on manifolds, 2019, in progress. (arXiv)

    10. (with T. R. Gao and L.-H. Lim) Semi-Riemannian manifold optimization, 2019, in progress. (arXiv)

    11. (with J. W. Nie and L. H. Zhi) Tensor decompositions on algebraic varieties, 2017, in progress. (arXiv)


          学术活动


            Seminar on Nonlinear Algebra & Data Science

            This is a seminar co-organized with Manolis C. Tsakiris. It aims to bring researchers in Algebra and Data Science together. Talks will be presented in English and everyone is welcome to our seminar! 

            2023/08/31 Beihui Yuan (BIMSA): An algebraic framework for geometrically continuous splines 

            Abstract: Geometrically continuous splines are piecewise polynomials defined on a collection of patches stitched together through transition maps. In this talk, we introduce an algebraic framework to study geometrically continuous splines. This framework enables us to use algebraic tools to analysis the dimension of spline spaces, and to present a new algorithm to construct bases using algebraic methods. This talk is based on a joint work with Angelos Mantzaflaris, Bernard Mourrain and Nelly Villamizar.

            学术报告（2018年 -- 至今）
            • Algebraic geometry and complexity theory workshop, Warsaw, Poland (2022)
            • Conference on Applied Geometry for Data Sciences, Chongqing, China (2022)
            • Minisymposium on Algebra and Geometry of Tensors: structured tensors, SIAM Conference on Applied Algebraic geometry, College Station, Texas, USA (2021)
            • Minisymposium on Linear Algebra and Differential Geometry, 2021 SIAM Conference on Applied Linear Algebra, New Orleans, Louisana, USA (2021)
            • Data Science Seminar, Mathematical Institute, Orxford University, Oxford, UK (2021)
            • Minisymposium on Tensors, 2019 SIAM Conference on Applied Algebraic Geometry, Bern, Switzerland (2019)
            • Minisymposium on Numerical Differential Geometry, 2019 SIAM Conference on Applied Algebraic Geometry, Bern, Switzerland (2019)
            • Computational and Applied Mathematics Colloquium, University of Chicago, Chicago, Ilinois, USA (2018)
            • Session on Polynomial and Tensor Optimization, 23rd Minisymposium on Mathematical Programming, University of Bordeaux, Bordeaux, France (2018)
            • Minisymposium on Geometry of Tensors, 2018 SIAM Annual Meeting, Oregon Convention Center, Portland, Oregon, USA (2018)
            • 7 th International Conference on Computational Harmonic Analysis, Nashville, Tennessee, USA (2018)

            • Minisymposium on Tensor Analysis, Computation, and Applications, SIAM Conference on Applied Linear Algebra, HongKong, China (2018)


            合作情况

            中国

            黄巧龙，山东大学

            胡胜龙，杭州电子科技大学

            高小山，中科院数学与系统科学研究院

            支丽红，中科院数学与系统科学研究院

            美国

            Lek-Heng Lim, University of Chicago

            Joseph M. Landsberg, Texas A&M University

            Jiawang Nie, University of Berkeley at San Diego

            Jeffrey Uhlmann, University of Missouri

            Zehua Lai, University of Chicago

            Zhen Dai, University of Chicago 

            Ken Sze-Wai Wong, University of Chicago

            Tingran Gao, University of Chicago

            法国

            Pierre Comon, CNRS

            Yang Qi, CMAP, Ecole Polytechnique

            英国

            Mu Niu, University of Glasgow

            Rodolphe Sepulchre, University of Cambridge

            指导学生

            现指导学生

            刘鹏  博士研究生  070104-应用数学  

            陈琦元  硕士研究生  070104-应用数学  

            王立夏  硕士研究生  070104-应用数学  

            王愚  博士研究生  070104-应用数学  

            科研项目

            • 中国科学院稳定支持基础研究领域青年团队（10人），1500万，课题组成员，2021-2026
            • 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，基于流形的数据压缩和传输算法，72万, 课题负责人，2021--2022
            • 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
            • 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
            • 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
            • 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

            获得荣誉

            • 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，2023
            • 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