职称/职务:教授
E - mail: jikuikui@163.com jikui@hebtu.edu.cn
研究领域: 泛函分析(算子理论)
来校时间:2008年
个人简介:
1981年4月23日出生,男,汉族,山东省郯城县人。理学博士,博士生导师。自2002年起,师从著名算子理论专家蒋春澜教授从事算子理论的研究,主要关注复几何在线性算子理论中的应用,研究内容包括Cowen-Douglas算子与Hermitian全纯向量丛的结构与分类问题,包括利用几何不变量刻画算子的酉分类与相似分类、Cowen-Douglas 理论在C*代数中的拓展与应用、算子的相似分类与Corona问题等。相关成果被Advances in Mathematics、Journal of Functional Analysis、Israel Journal of Mathematics、Journal of Noncommutative Geometry、Journal of Operator Theory、Canadian Journal of Mathematics、Illinois Journal of Mathematics、European Journal of Mathematics、Studia Mathematica等数学期刊发表,并在应邀在2018年度、2023年度IWOTA(国际算子理论会议)作学术报告。
教育背景(Educational background):
博士,算子理论与算子代数,金沙集团1862cc橙色,2005-2008
Doctor, operator theory and operator algebra, Hebei Normal University, 2005-2008
硕士,算子理论与算子代数,河北工业大学,2002-2005
Master, operator theory and operator algebra, Hebei University of technology, 2002-2005
学士,数学,聊城大学,1998-2002
Bachelor of mathematics, Liaocheng University, 1998-2002
访问经历(Visit):
访问学者,菲尔兹研究所(加拿大),2007
Visiting scholar, Fields Institute (Canada), 2007
访问学者,波多黎各大学(美国),2009
Visiting scholar, University of Puerto Rico (USA), 2009国家公派访问学者,Indian Institute of Science (印度); 2012
National public visiting scholar, Indian Institute of Science (India); 2012
复几何与算子理论国际会议,Indian Statistical Institute(印度),2015
Complex Geometry and Operator Theory`,Indian Statistical Institute(India),2015
IWOTA(2023),赫尔辛基大学(芬兰),2023
IWOTA(2023),University of Helsinki (Finland), 2023
教学情况(Courses):
本科生课程:《高等数学》、《数学分析》、《复变函数》、《线性代数》、《分析方法选讲》
Undergraduate:《Calculus》、《Mathematical Analysis》、《Complex Analysis》、《Linear Algebra》、《Advanced Calculus》
研究生课程:《算子理论》、《C*代数》、《复几何与算子理论》
Graduate student:《Operator Theory》、《C*-algebras》、《Complex geometry and operator theory》
科研情况:
1:科研项目(Grants)
(1)国家自然科学基金青年基金:算子代数的分类,批准号:10901046,2010-2012(已结题);主持人
(2)国家自然科学基金面上项目:曲率,第二基本形式与几何算子的相似性的研究,批准号:11471094,2015-2018(已结题)主持人;
(3)高等学校全国百篇优秀博士学位论文作者专项资金,2010-2012,(已结题)主持人;
(4)河北省杰出青年基金;拟齐次曲线的相似分类,批准号:A2016205219,2016-2018(已结题)主持人;
(5)河北省2014年青年拔尖人才;复几何在算子代数中的应用,批准号BJ2014037,2015-2017,(已结题)主持人;
(6)国家自然科学基金重点项目:算子代数中的几何与分类理论,批准号11831006,2019-2023, (已结题) 参与人;
(7)国家自然科学基金优秀青年基金项目:算子理论与算子代数,批准号:11922108,2020-2022(已结题)主持人;
(8)国家自然科学基金重点国际(地区)合作研究项目:单的与非单的顺从代数的分类及其应,批准号:11920101001,2020-2024(在研)参与人;
(9)国家自然科学基金面上项目:Cowen-Douglas算子组的相似不变量,批准号:12371129,2024-2027(在研)主持人.
2:学术论文(Publication):
(1)Jiang, Chunlan, Guo, Xianzhou, and Ji, Kui., K-group and similarityclassification of operators. J. Funct.Anal. 225 (2005), no.1 , 167--192.
(2)Jiang, Chunlan and Ji, Kui. Similarity classification of holomorphic curves. Adv. Math. 215 (2007), no.2 , 446--468.
(3)He, Hua and Ji, Kui., Strongly irreducible decomposition and similarity classification of operators. Illinois. J. Math 51 (2007), no.2, 409—428.
(4)Ji, Kui and Jiang, Chunlan, A complete classification of AI algebra with the ideal property, Canada. J. Math. 63, No.2,381-412 (2011).
(5)Ji, Kui, Similarity classification and properties of some extended holomorphic curves. Integral Equations and Operator Theory 69 (2011), no.1,133–148.
(6)Jiang, Chunlan; Ji, Kui .Theory of strongly irreducible operators and its applications. Adv. Math.《数学进展》(China)40 (2011), no.4, 385–392.
(7)Ji Kui, Shi Rui, Similarity of multiplication operators on the Sobolev disk algebra. Acta. Math. Sin. (Engl. Ser.)29 (2013), no.4, 789–800.
(8)Ji Kui, On a generalization of B_1(\Omega) on C*-algebras, Proc. Indian Acad. Sci. Math. Sci. Vol 124. no.2. May (2014),243-253.
(9)Ji, Kui, Jiang, Chunlan, Dinesh Kumar Keshari, Gadadhar Misra, Flag structure for operators in the Cowen-Douglas class, C.R.Acad.Sci.Paris.Ser. I, 352 (2014) 511-514.
(10)Hou, Yingli and Ji, Kui On the extended holomorphic curves on C* algebras. Oper. Matrices 8 (2014), no. 4,999–1011.
(11)Dai, Hong; Hou, Yingli and Ji, Kui A note on curvature and similarity of some CowenDouglas operators. J. Math. Anal.Appl. 444 (2016), no.1, 167–181.
(12)Hou, Yingli; Ji, Kui and Kwon, HyunKyoung The trace of the curvature determines similarity. Stud. Math.236, no.2, 193-200 (2017).
(13)Ji, Kui, Jiang, Chunlan, Dinesh Kumar Keshari, Gadadhar Misra, Rigidity of the flag structure for a class of Cowen-Douglas operators. J. Funct. Anal. 272 (2017), no.7, 2899–2932.
(14)Jiang, Chunlan, Ji, Kui, Gadadhar Misra, Classification of quasihomogeneous holomorphic curves and operators in the Cowen-Douglas class. J. Funct. Anal. 273 (2017), no.9,2870–2915.
(15)Ji, Kui. Curvature formulas of holomorphic curves on C*-algebras and Cowen-Douglas operators. Complex Anal. Oper. Theory 13 (2019), no.4, 1609–1642.
(16)Ji,Kui Jaydeb Sarkar, Similarity of quotient Hilbert modules in the Cowen–Douglasclass, European Journal of Mathematics,5 (2019), no.4, 1331–1351.
(17)Tian, Liang, Guo, Wei and Ji, Kui, A note on a subclass of Cowen-Douglas operators, Acta Mathematica Sinica, English Series, 35 (2019), no.11, 1795–1806.
(18)Ji, Kui, Hyun-Kyoung Kwon, and Xu, Jing, N-hypercontractivity and similarity of Cowen-Douglas operators, Linear Algebra Appl. 592 (2020), no. 1, 20–47.
(19)Jiang, Chunlan, Ji, Kui, Integral curvature and similarity of Cowen-DouglasOperators, In: Curto R.E., Helton W., Lin H., Tang X., Yang R., Yu G. (eds)Operator Theory,Operator Algebrasand Their Interactions with Geometry and Topology. Operator Theory: Advances and Applications, 278 (2020),373-390.
(20)Ma,Zhenhua, Ji, Kui and Li, Yucheng, Compact operators under Orlicz functions, Indian Journal of Pure and Applied Mathematics, 51(2020), no.4, 1633–1649.
(21)Hou, Yingli, Ji, Kui and Zhao, Linlin, Factorization of generalized holomorphic curve and homogeneity of operators, Banach. J. Math. Anal. 15 (2021), no. 2, Paper No. 43, 23 pp.
(22)Jiang, Chunlan, Ji, Kui and Wu, Jinsong, Similarity Invariants of Essentially normal Cowen-Douglas Operators and Chern Polynomials , Israel Journal of Mathematics,248,(2022)229–270.
(23)Ji,Kui and Ji, Shanshan, The metrics of Hermitian holomorphic vector bundles and the similarity of Cowen-Douglas operators,Indian Journal of Pure and Applied Mathematics, 53 (2022), no. 3, 736–749.
(24)Ji, Kui, Hyun-Kyoung Kwon, Jaydeb Sarkar,and Xu, Jing, A subclass of the Cowen-Douglas class and similarity, Mathematische Nachrichten, 295(2022), no.11, 2197–2222.
(25)Ji,Kui and Ji, Shanshan, A note on unitary equivalence of operators acting onreproducing kernel Hilbert spaces, Houston Journal of Mathematics, 48(2022),no.1,125-148.
(26)Jiang,Chunlan, Ji, Kui and Dinesh Kumar Keshari, Geometric Similarity invariants of Cowen-Douglas Operators, Journal of Noncommutative Geometry, 17(2023),no.2,pp.573-608.
(27)Hou, Yingli, Ji, Kui, Ji, Shanshan and Xu, Jing, Geometry of holomorphic vector bundles and similarity of commuting operator tuples, Journal of Operator Theory, 91(2024), no.1, 169-202.
(28)Jiang,Chunlan, Fang, Junsheng and Ji Kui, Cowen Douglas operators and the third of Halmos' ten problems,Israel Journal of Mathematics, to appear.
(29)Yang, Jianming and Ji, Kui, On the similarity of powers of operators with flag structure, Proceedings of the American Mathematical Society, to appear.
(30)Xie, Yufang and Ji, Kui, Operators of the Cowen-Douglas class with strong flag structure, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas,to appear.
(31)Ji,Kui, Ji, Shanshan,Dinesh Kumar Keshari,and Xu, Jing, On the similarity of restriction of the operator to an invariant subspace, arXiv:2012.13535.
(32)Ji, Kui, Ji, Shanshan, Hyun-Kyoung Kwon and Xu, Jing, The Cowen-Douglas theory for operator tuples and similarity, arXiv:2210.00209.
(33) Ji,Kui, Ji, Shanshan and Xu, Jing, Geometry of holomorphic vector bundles and similarity of commuting operator tuples II, in prepare.
(34)Ji, Kui, Ji, Shanshan and Xu, Jing, The Cowen-Douglas theory for operator tuples and similarity II, in prepare.
(35)Ji,Kui, Ji, Shanshan, Hyun-Kyoung Kwon, Liu, Xiaoceng and Xu, Jing, On the metric of the jet bundle and similarity of multiplication operators on Dirichlet spaces,arXiv:2401.13281.
(36)Ji, Kui and Xu, Jing, K-theory and similarity of Cowen Douglas operator tuples, in prepare.