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。

2017-08--至今, 中科院数学与系统科学研究院，副研究员
2015-09--2017-07, University of Chicago, 博士后
2012-09--2015-08, University of Chicago, L. E. Dickson Instructor

2023-01--至今, SIAM Journal on Applied Algebra and Geometry, Associate Editor

(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
(with S. W. Wong and L.-H. Lim) Optimization on flag manifolds, Mathematical Programming (Series A),  2022, 194(1-2), pp. 621--660. (arXiv)
(with L.-H. Lim and S. W. Wong) The Grassmannian of affine subspaces, Foundations of Computational Mathematics, 2021, 21, pp. 537--574. (arXiv)
(with P. Comom, L.-H. Lim and Y. Qi) Topology of tensor ranks, Advances in Mathematics, 2020, 367, pp. 107128. (arXiv)
(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)
(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)
(with J. W. Nie) Hankel tensor decompositions and ranks, SIAM Journal on Matrix Analysis and Applications, 2019, 40(2), pp. 486--516. (arXiv)
(with L.-H. Lim) Fast structured matrix computations: tensor rank and Cohn-Umans method, Foundations of Computational Mathematics, 2018, 18(1), 45--95. (arXiv)
(with L.-H. Lim) Cohomology of cryo-electron microscopy, SIAM Journal on Applied Geometry and Algebra, 2017, 1(1), pp. 507--535. (arXiv)
(with S. L. Hu) Inverse eigenvalue problems for tensors, Communications in Mathematical Sciences, 2017, 15(6), pp. 1627--1649. (arXiv)
New classes of matrix decompositions, Linear Algebra and its Applications, 2017, 514, pp. 47--81. (arXiv)
(with L.-H. Lim) Every matrix is a product of Toeplitzmatrices, Foundations of Computational Mathematics, 2016, 16(3), pp. 577--598. (arXiv)
(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)
(with S. L. Hu) Multiplicities of tensor eigenvalues, Communications in Mathematical Sciences, 2016, 14(4), pp. 1049--1071. (arXiv)
(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)
The stabilizers of immanants, Linear Algebra and Its Applications, 2011, 435(5), pp. 1085--1098. (arXiv)

(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.
(with Y. Qi, P. Comon and L.-H. Lim) Path connectedness of tensor ranks, 27th European Signal Processing Conference (EUSIPCO 2019), pp. 1-5.
(with L.-H. Lim) Algorithms for structured matrix-vector product of optimal bilinear complexity, 2016 IEEE Information Theory Workshop (ITW), pp. 310-314.

1. (with Q. Y. Chen and J. Uhlmann) Generalizing Frobenius inversion to quaternion matrices, 2023, submitted. (arXiv) 
2. (with Qiao-Long Huang and Xiao-Shan Gao) Skew-sparse matrix multiplication, 2022, submitted. (arXiv)
3. (with S. L . Hu) When geometry meets optimization theory: partially orthogonal tensors, 2022, submitted. (arXiv)
4. (with J. T. Yang and L. H. Zhi) Lower bounds of functions on finite abelian groups, 2023, in progress. (arXiv)
5. (with Z. H. Lai and  L.-H. Lim) Simpler flag optimization, 2022, in progress. (arXiv)
6. (with Z. Dai and L.-H Lim) Inverting a complex matrix, 2022, in progress. (arXiv) 
7. (with J. T. Yang and L. H. Zhi) Short certificates for MAX-SAT via Fourier  sum of squares, 2022, in progress. (arXiv)
8. (with Z. H. Lai and  L.-H. Lim) Simpler Grassmannian optimization, 2022, in progress. (arXiv)
9. (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) 
10. (with L.-H. Lim) Tensor network states ranks, 2021, in progress. (arXiv)
11. (with M. Niu and P. Cheung) Heat kernel and intrinsic Gaussian processes on manifolds, 2019, in progress. (arXiv)
12. (with T. R. Gao and L.-H. Lim) Semi-Riemannian manifold optimization, 2019, in progress. (arXiv)
13. (with J. W. Nie and L. H. Zhi) Tensor decompositions on algebraic varieties, 2017, in progress. (arXiv)

1. Algebraic geometry and complexity theory workshop, Warsaw, Poland (2022)
2. Conference on Applied Geometry for Data Sciences, Chongqing, China (2022)
3. Minisymposium on Algebra and Geometry of Tensors: structured tensors, SIAM Conference on Applied Algebraic geometry, College Station, Texas, USA (2021)
4. Minisymposium on Linear Algebra and Differential Geometry, 2021 SIAM Conference on Applied Linear Algebra, New Orleans, Louisana, USA (2021)
5. Data Science Seminar, Mathematical Institute, Orxford University, Oxford, UK (2021)
6. Minisymposium on Tensors, 2019 SIAM Conference on Applied Algebraic Geometry, Bern, Switzerland (2019)
7. Minisymposium on Numerical Differential Geometry, 2019 SIAM Conference on Applied Algebraic Geometry, Bern, Switzerland (2019)
8. Computational and Applied Mathematics Colloquium, University of Chicago, Chicago, Ilinois, USA (2018)
9. Session on Polynomial and Tensor Optimization, 23rd Minisymposium on Mathematical Programming, University of Bordeaux, Bordeaux, France (2018)
10. Minisymposium on Geometry of Tensors, 2018 SIAM Annual Meeting, Oregon Convention Center, Portland, Oregon, USA (2018)
11. 7 th International Conference on Computational Harmonic Analysis, Nashville, Tennessee, USA (2018)
12. Minisymposium on Tensor Analysis, Computation, and Applications, SIAM Conference on Applied Linear Algebra, HongKong, China (2018)
13. The 2017 Korea-China International Conference on Matrix Theorem and Application, Sungkyunkwan university, Suwon, Korea (2017)
14. Minisymposium on Tensors: From Algebra to Applications, SIAM Conference on Applied Algebraic Geometry, Atlanta, Georgia, USA (2017)
15. Minisymposium on Geometry and Computational Challenges in Data Science, SIAM Annual Meeting, David Lawrence Convention Center, Pittsburgh, Pennsylvania, USA (2017)
16. 2017 Meeting of the International Linear Algebra Society, Iowa State University, Ames, Iowa, USA (2017)
17. Algebra Seminar, School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia, USA (2017)
18. Householder Symposium XX on Numerical Linear Algebra, the Inn at Virginia Tech, Blacksburg, Virginia, USA (2017)
19. Colloquium, Department of Mathematics, University of Minnesota--Twin Cities, Minneapolis, Minnesota, USA (2017)
20. Applied Algebra Seminar, Department of Mathematics, University of Wisconsin--Madison, Madison, Wisconsin, USA (2017)
21. Optimization Seminar, Department of Mathematics, University of California at San Diego, La Jolla, California, USA (2017)

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

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  

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• 华为技术合作成果转化二等奖，2023. 04

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