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 in Indiana Univ. Math. J.

• Castelnuovo-Mumford regularity of FI^m-modules presented in finite degrees, J. Algebra 555 (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. Algebra 223 (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. Algebra 223 (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. Algebra 501 (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. Algebra 472 (2017), 369-398.

• On compact exceptional objects in bounded derived module categories, J. Algebra 463 (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. Algebra 420 (2014), 217-241.

• On the representation types of category algebras of finite EI categories, J. Algebra 402 (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. Algebra 345 (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