基本信息

姓名：蒋凯

职称：教授

电子信箱：kaijiang@xtu.edu.cn

办公室：数学楼 B-511

个人简介

蒋凯，教授，国家高层次青年人才；主要从事丢番图误差数学、算法及应用等方面的研究；主持国家重点研发计划课题1项、湖南省科技创新领军人才项目、国家自然科学基金3项（面上2项、青年1项）、湖南省杰出青年基金；获宝钢优秀教师奖、中国计算数学学会优秀青年论文一等奖；湖南省优秀博士论文指导教师；《计算数学》编委。

学习工作经历

教育经历：

2002.09-2006.06, fun88乐天使，本科，                 信息与计算科学

2006.09-2011.06, fun88乐天使，博士研究生，   计算数学

2007.01-2011.06, 北京大学，博士研究生，   计算数学，    联合培养

工作经历：

2020.01 至今，     fun88乐天使，                  教 授

2015.01-2019.12，fun88乐天使，                副教授

2015.08-2017.12，新加坡国立大学，   客座研究员

2013.07-2014.12，fun88乐天使，                讲 师

2011.07-2013.06，北京大学，                博士后

主讲课程

本科生课程：

《高等代数I、II》、《复变函数》、《实变函数》、《高等数学》、《线性代数》等

研究生课程：

《软物质材料科学计算导论》、《常微分方程定性理论》、《最优化计算》等

研究方向

• 无理数引发的数学和算法

研究简介：数是数学研究的基石，也是理解自然现象的基础。实数由零测度的有理数集和满测度的无理数集构成。因此，无论是在数学研究还是自然现象中，无理数都起到了关键作用。事实上，许多体系及现象都是无理数起主导作用，例如三体问题的运行轨迹、准晶、多晶材料、准（拟）周期量子系统、莫尔光学、波的碰撞、魔角石墨烯、局域化等。然后，目前的计算机只能存储有限位（即有理数），难以存储和表示无理数（无限不循环的数），这给数值计算带来了巨大挑战。求解此类系统时，已有的周期逼近算法（亦称超原胞法）会引入丢番图误差——即有理数逼近无理数产生的误差，该误差会对计算结果的准确性起决定性影响。为解决这一困难，我们课题组发展了一系列新的计算方法，避免了丢番图误差，将高精度数值计算从有理数域扩展到了实数域，在数学上建立了算法的严格理论。同时，我们将算法运用到了准晶、非公度相变、界面、准周期量子系统、准周期均匀化问题等多种无理数起主导体系体系的研究中，不仅展现了算法的高精度和高效性，更重要地是揭示了新的现象和规律。

• 软物质体系可计算建模与模拟

• AI for Science

招生方向

课题组长期招收优秀的博士后、数学类博士生、数学类学术硕士生、应用统计专业硕士生和本科生。欢迎对科学研究感兴趣，具有强大自驱力、良好数学基础、编程和写作能力，并具有恒心和毅力的同学加入课题组！

代表性论文

[30] Tianyi Tan, Yu Cao, Changlong Chen, Sanliang Ling, Gaolei Hou, Martin J. Paterson, Xin Wang, Ying Chen, Kai Jiang, Gang He, Goran Ungar, Georg H. Mehl and Feng Liu,Tuning aggregation in liquid-crystalline squaraine chromophores, Advanced Science, 2416249, 2025.

[29] Wenwen Zou, Juan Zhang, Jie Xu, Kai Jiang, Quasiperiodic [110] symmetric tilt FCC grain boundaries, Computational Materials Science, 253: 113811, 2025.

[28] Dan Wei, Zhijuan He, Yunqing Huang, An-Chang Shi, Kai Jiang, Theoretical study on self-assembly structures in X-shaped liquid crystalline macromolecules, The Journal of Chemical Physics, 162: 114904, 2025.

[27] Chen Cui, Kai Jiang, Shi Shu, A neural multigrid solver for Helmholtz equations with high wavenumber and heterogeneous media, SIAM Journal on Scientific Computing, 47(3): C655-C679, 2025.

[26] Kai Jiang, Xueyang Li, Yao Ma, Juan Zhang, Pingwen Zhang, Qi Zhou, Irrational-window-filter projection method and application to quasiperiodic Schrödinger eigenproblems, SIAM Journal on Numerical Analysis, 63(2): 564-587, 2025.

[25] Kai Jiang, Shifeng Li, Pingwen Zhang, On the approximation of quasiperiodic functions with Diophantine frequencies by periodic functions, SIAM Journal on Mathematical Analysis, 57(1): 951-978, 2025.

[24] Gang Cui, Kai Jiang, Tiejun Zhou, An efficient saddle dynamic method for ordered phase transition involving translational invariance, Computer Physics Communications, 306, 109381, 2025.

[23] Gang Cui, Kai Jiang, Spring pair method of finding saddle points using the minimum energy path as a compass, Physical Review E, 110, 064123, 2024

[22] Zhijuan He, Jin Huang, Kai Jiang, An-Chang Shi, The morphologies of symmetric diblock copolymers in the 3D soft confinement, Soft Matter, 20, 9404-9412, 2024.

[21] Tiejun Zhou, Lei Zhang, Pingwen Zhang, An-Chang Shi, Kai Jiang, Nucleation and phase transitions of decagonal quasicrystals, The Journal of Chemical Physics, 161, 164503, 2024.

[19] Zhijuan He, Xin Wang, Pingwen Zhang, An-Chang Shi and Kai Jiang, Theory of polygonal phases self-assembled from T-shaped liquid crystalline molecules, Macromolecules, 57(5), 2154-2164, 2024.

[18] Kai Jiang, Qi Zhou, Pingwen Zhang, Accurately recovery global quasiperiodic systems by finite points,  SIAM Journal on Numerical Analysis, 62(4), 1713-1735, 2024.

[17] Chenglong Bao, Chang Chen, Kai Jiang, Lingyun Qiu, Convergence analysis for Bregmanian iterations in a class of Landau energy functionals, SIAM Journal on Numerical Analysis, 62(1), 476-499, 2024.

[16] Kai Jiang, Shifeng Li, Pingwen Zhang, Numerical methods and analysis for computing quasiperiodic systems, SIAM Journal on Numerical Analysis, 62(1), 353-375, 2024.

[15] Kai Jiang, Juan Zhang, Qi Zhou, Multitask kernel-learning parameter prediction method for solving time-dependent linear systems, CSIAM Transactions on Applied Mathematics, 4(4), 672-795, 2023.

[14] Kai Jiang, Xuehong Su, Juan Zhang, A general alternating-direction implicit framework with Gaussian regression parameter prediction for large sparse linear systems, SIAM Journal on Scientific Computing, 44(4): A1960-A1988, 2022.

[13] Kai Jiang, Wei Si, Jie Xu, Tilt grain boundaries of hexagonal structures: a spectral viewpoint, SIAM Journal on Applied Mathematics, 82(4): 1267-1286, 2022.

[12] Jianyuan Yin, Kai Jiang, An-Chang Shi, Pingwen Zhang, and Lei Zhang, Transition pathways connecting crystals and quasicrystals, Proceedings of the National Academy of Sciences, 118 (49)  2106230118, 2021.

[11] Kai Jiang, Wei Si, Chang Chen, Chenglong Bao, Efficient numerical methods for computing the stationary states of phase field crystal models, SIAM Journal on Scientific Computing, 43(6): B1350-B1377, 2020.

[10] Huayi Wei, Ming Xu, Wei Si, Kai Jiang, A finite element method of the self-consistent field theory on general curved surfaces, Journal of Computational Physics, 387: 230-244, 2019.

[9] Kai Jiang, Pingwen Zhang, Numerical mathematics of quasicrystals, Proc. Int. Cong. of Math., 3 (2018), pp. 3575–3594.

[8] Kai Jiang, Pingwen Zhang, An-Chang Shi, Stability of icosahedral quasicrystals in a simple model with two-length scales, Journal of Physics: Condensed Matter, 29:124003, 2017.

[6] Kai Jiang, Juan Zhang, Qin Liang, Self-assembly of asymmetrically interacting ABC star triblock copolymer melts, The Journal of Physical Chemistry B, 119: 14551-14562, 2015.

[5] Kai Jiang, Jiajun Tong, Pingwen Zhang, An-Chang Shi, Stability of two-dimensional soft quasicrystals in systems with two length scales, Physical Review E, 92: 042159, 2015.

[4] Kai Jiang, Weiquan Xu, Pingwen Zhang, Analytic structure of the SCFT energy functional of multicomponent block copolymers, Communications in Computational Physics, 17:1360-1387, 2015.

[3] Kai Jiang, Pingwen Zhang, Numerical methods for quasicrystals, Journal of Computational Physics, 256:428-440, 2014.

[1] Kai Jiang, Yunqing Huang, Pingwen Zhang, Spectral method for exploring patterns of diblock copolymers, Journal of Computational Physics, 229:7796-7805, 2010.