学校首页
设为收藏
李利平（Liping Li），男，博士，教授，博士生导师
教育背景：
B.S. in Chem., Jul. 1999, Tsinghua University, Beijing
Ph.D. in Math., Aug. 2012, University of Minnesota, Minneapolis
工作经历：
1999.07 - 2006.06, Product Manager, Director, Vice President in IT industry, Beijing, China
2006.08 - 2012.06, Teaching Assistant, School of Mathematics, University of Minnesota, Minneapolis, USA
2012.07 - 2015.06, Visiting Assistant Professor, University of California, Riverside, USA
2015.07 - , Professor, Hunan Normal University, Changsha, China
教学育人：
Undergraduate course: Modern Algebra
Graduate courses: Commutative Algebra, Representation Theory of Finite Groups, An Overview of Modern Mathematics
Currently I am tutoring 2 Ph.D. students and 4 Master students. Prospective students interested in my research area please send me an email briefly introducing yourself. Prerequisites include: a solid background on abstract algebra, combinatorics, and elementary topology; moderate English reading and writing ability.
科学研究：
I am interested in representation theory, noncommutative rings, homological algebra, group theory, and algebraical combinatorics. Currently I am working on representation theory of infinite combinatorial categories, as well as its application in representation stability theory.
Grants:
Homological degrees of representations of categories with shift functors, NSFC 11541002, 2016.01-2016.12
Representation theoretic and homological properties of categories in representation stability theory, NSFC 11771135, 2018.01-2021.12
HuXiang High-Level Talents Gathering Program, the Science and Technology Department of Hunan Province, 2019RS1039, 2019.08-2021.07
Selected Papers:
A full list of publications is available at mathscinet or arXiv (with tag math.RT).
An application of Nakayama functor in representation stability theory, (with WL Gan and CC Xi), to appear inIndiana Univ. Math. J.
Castelnuovo-Mumford regularity of FI^m-modules presented in finite degrees,J. Algebra555 (2020), 246–264.
Linear stable range for homology of congruence subgroups via FI-modules, (with WL Gan),Selecta Math. (N.S.)25 (2019), Art. 55, 11 pp.
FI^m-modules over Noetherian rings, (with N. Yu),J. Pure. Appl. Algebra223 (2019), 3436-3460.
An Inductive machinery for representations of categories with shift functors, (with WL Gan),Trans. Amer. Math. Soc.371 (2019), 8513-8534.
Asymptotic behavior of representations of graded categories with inductive functors, (with WL Gan),J. Pure Appl. Algebra223 (2019), 188-217.
Depth and the local cohomology of FI_G-modules, (with E. Ramos),Adv. Math.329 (2018), 704-741.
Koszulity of directed categories in representation stability theory, (with WL Gan),J. Algebra501 (2018), 88-129.
Homological degrees of representations of categories with shift functors,Trans. Amer. Math. Soc.370 (2018), 2563-2587.
On central stability, (with WL Gan),Bull. Lond. Math. Soc.49 (2017), 449-462.
Filtrations and homological degrees of FI-modules, (with N. Yu),J. Algebra472 (2017), 369-398.
On compact exceptional objects in bounded derived module categories,J. Algebra463 (2016), 234-253.
Coinduction functor in representation stability theory, (with WL Gan),J. Lond. Math. Soc.92 (2015), 689-711.
Representations of modular skew group algebras,Trans. Amer. Math. Soc.367 (2015), 6293-6314.
A generalized Koszul theory and its relation to the classical theory,J. Algebra420 (2014), 217-241.
On the representation types of category algebras of finite EI categories,J. Algebra402 (2014), 178-218.
A generalized Koszul theory and its application,Trans. Amer. Math. Soc.366 (2014), 931-977.
A characterization of finite EI categories with hereditary category algebras,J. Algebra345 (2011), 213-241.
Selected Talks
Representation stability theory and its categorification,the 15th National Algebra Conference, Nanning, 2019.07
Linear stable range of homology groups of congruence subgroups,the 8th International Conference on Representation Theory, Haerbin, 2019.07
A local cohomology theory of FI-modules,the Joint International Meeting of AMS and CMS, Shanghai, 2018.06
A homological approach to representation theory of FI,Workshop on Combinatorial Categories in Algebra and Topology, Osnabruck University, Germany, 2018.11
A criterion for local Noetherianity of infinite EI categories,Algebra Seminar, Chinese Science and Technology University, Hefei, 2018.06
Asymptotic behavior of homology groups of congruence subgroups,Algebra Seminar, Tsinghua University and Mathematical Institute of the Chinese Academy of Science, Beijing, 2018.01
A homological approach to representation theory of FI,the 14th National Algebra Conference, Yangzhou, 2016.05
Serial lectures on representation stability theory,the 18th Workshop on Algebraic Representation Theory, Nanjing, 2016.06
Koszulity of directed categories in representation stability theory,Conference on Geometric Methods in Representation Theory, University of Iowa, 2014.11
Homological dimensions of crossed products,Maurice Auslander International Conference, Woods Hole, USA, 2014.4
A generalized Koszul theory and its application,the 2nd Pacific Rim Mathematical Conference, Shanghai, 2013.06
A generalized Koszul theory and its application,the 6th Southeastern Lie Theory Workshop, Louisiana State University, 2013.05
Representations of modular skew group algebras,Maurice Auslander International Conference, Woods Hole, USA, 2013.5
Applications of generalized Koszul theory in representation theory of EI categories,University of California, San Diego, 2012.11
所获荣誉及学术兼职：
Distinguished Professor of the Hunan Provincial Furong Scholars Program, 2019
One of the Chosen Top Ten Faculty Members and Staffs of Hunan Normal University, 2019
Member of the Chinese People's Political Consultative Conference Hunan Provincial Committee, 2018 -
Member of the Standing Committee of the Hunan Provincial Federation of Overseas Chinese, 2019 -
兴趣爱好：
Reading: History, Philosophy, Social Sciences, Literature
Classical Music: symphonies, concertos, symphonic poems.
联系方式：lipingli@hunnu.edu.cn