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李利平

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Liping Li
Professor of Mathematics,
College of Mathematics and Computer Science,
Hunan Normal University, Changsha, Hunan 410081, China
email: lipingli(at)hunnu(dot)edu(dot)cn.

B.S. in Chem., Jul. 1999, Tsinghua University, Beijing.
Ph.D. in Math., Aug. 2012, 
University of Minnesota, Minneapolis.

2012 - 2015, Visiting Assistant Professor, University of California, Riverside, USA.
2015 - , Professor, Hunan Normal University, Changsha, China.
承担课题: 

2016/01 - 2016/12, "Homological degrees of representions of categories with shift functors", NSFC 11541002, PI.
2018/01 - 2021/12, "On representional and homological properties of categories in representation stability theory", NSFC 11771135, PI.

近期发表的代表性论文: 

A characterization of finite EI categories with hereditary category algebras, J. Algebra 345 (2011), 213-241.
      Extention algebras of standard modules, Comm. Algebra 41 (2013), 3445-3464.
      Algebras stratified for all linear orders, Alg. Repn. Theory 16 (2013), 1085-1108.
      A generalized Koszul theory and its application, Trans. Amer. Math. Soc. 366 (2014), 931-977.
      On the representation types of category algebras of finite EI categories, J. Algebra 402 (2014), 178-218.
      A generalized Koszul theory and its relation to the classical theory, J. Algebra 420 (2014), 217-241.
      Stratifications of finite directed categories and generalized APR tilting modules, Comm. Algebra 43 (2015), 1723-1741.
      Representations of modular skew group algebras, Trans. Amer. Math. Soc. 367 (2015), 6293-6314.
      Finitistic dimensions and piecewise hereditary property of skew group algebras, Glasgow Math. J. 57 (2015), 509-517.
      Noetherian property of infinite EI categories, (with WL Gan), New York J. Math. 21 (2015), 369–382.
      Coinduction functor in representation stability theory, (with WL Gan), J. Lond. Math. Soc. 92 (2015), 689-711.
      On compact exceptional objects in bounded derived module categories, J. Algebra 463 (2016), 234-253.
      Upper bounds of homological invariants of FI_G-modulesArch. Math. (Basel) 107 (2016), 201-211.
      A remark on FI-module homology,
(with WL Gan), Mich. Math. J. 65 (2016), 855-861.
      Filtrations and homological degrees of FI-modules
, (with N. Yu), J. Algebra 472 (2017), 369-398.
      
Homological dimensions of crossed productsGlasgow Math. J. 59 (2017), 401-420.
      On central stability, (with WL Gan), Bull. Lond. Math. Soc. 49 (2017), 449-462.
      Derived equivalences between triangular matrix algebras,
to appear in Comm. Algebra.
      Homological degrees of representations of categories with shift functors, to appear in Trans. Amer. Math. Soc.
      Koszulity of directed categories in representation stability theory, (with WL Gan), submitted.
      Depth and the local cohomology of FI_G-modules, (with E. Ramos), submitted.
      
Two homological proofs of the Noetherianity of FI_G, submitted.
      An inductive machinery for representations of categories with shift functors, (with WL. Gan), submitted.
      
Asymptotic behaviors of representations of graded categories with inductive functors, (with WL. Gan), submitted.
      FI^
m-modules over Noetherian rings, (with N. Yu), submitted.
      An application of Nakayama functor in representation stability theory, (with WL Gan and CC Xi), submitted.
      Bounds on homological invariants of VI-modules, (with WL Gan), preprint.
      Local cohomology and the multi-graded regularity of FI^m-modules, (with E. Ramos), preprint.

教学情况: 

I am teaching Modern Algebra in Fall 2017.

Office: 617C
    Office hour: 13:30 - 14:30, Thursday; or make an appoitment via email.
    Grading Policy: homework assignments (20%), a midterm exam (20%), and a final exam (60%). 
    References: Open course at Harvard, Lecture notes I (Dartmouth Univ.), Lecture notes II (MIT)

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