李利平，男，湖南師範大學“瀟湘學者”特聘教授。
曾任加州大學河濱分校數學系訪問助理教授，主要從事代數表示論、同調代數、非交換環論的研究。
主要學術兼職：美國數學協會會員、Mathreview評論員、若干雜誌特約審稿。
基本介紹
- 中文名：李利平
- 國籍：中國
- 職業：湖南師範大學教授
- 畢業院校：清華大學
- 研究方向：代數
人物經歷,教育科研,研究領域,研究方向,發表論文,
人物經歷
1995-1999，清華大學化學系本科，獲得學士學位；
1999-2006，北京信息技術企業頻道經理、產品經理、部門經理、副總裁等。
2006-2012，明尼蘇達大學數學院研究生，獲得碩士及博士學位；同時擔任學院助教。
2012至今，任加州大學河濱分校數學系訪問助理教授。
教育科研
研究領域
研究範圍廣泛，包括代數表示論、同調代數、非交換環論、群論、代數組合等。在廣義Koszul理論、模斜群的表示與同調性質、範疇的表示與同調性質、代數的導出範疇等前沿領域均取得重要進展。系統將範疇表示論的思想引入表示穩定性理論這一國際最新領域並取得重要突破，為眾多範疇的重要性質給出了統一的概念性證明。獨立撰寫論文12篇，已發表或接受發表11篇；另合作撰寫5篇。均發表於國際知名期刊。與美國及加拿大若干知名高校的眾多教授建立了廣泛的學術交流與合作。成果受到包括史丹福大學、芝加哥大學、威斯康星大學等眾多同行的充分肯定與引用，先後多次在各類學術會議上做專題報告。
研究方向
I am interested in representation theory,noncommutative rings,homological algebra,group theory, andalgebraical combinatorics.Currently I am working on representation theory of infinite combinatorial categories, as well as its application in representation stability theory.
To better understand what representation stability theory is and its trends, please refer to the Representation Stability References assembled by Putman, Sam, Speyer, and Snowden.
發表論文
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-modules,Arch. Math. (Basel) 107 (2016), 201-211.
A remark on FI-module homology, (withWL Gan),Mich. Math. J. 65 (2016), 855-861.
Filtrations and homological degrees of FI-modules,(withN. Yu), J. Algebra 472 (2017), 369-398.
Derived equivalences between triangular matrix algebras, to appear in Comm. Algebra.
Homological dimensions of crossed products, to appear in Glasgow Math. J.
Homological degrees of representations of categories with shift functors, to appear in Trans. Amer. Math. Soc.
On central stability, (withWL Gan), to appear in Bull. Lond. 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), preprint.
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-modules,Arch. Math. (Basel) 107 (2016), 201-211.
A remark on FI-module homology, (withWL Gan),Mich. Math. J. 65 (2016), 855-861.
Filtrations and homological degrees of FI-modules,(withN. Yu), J. Algebra 472 (2017), 369-398.
Derived equivalences between triangular matrix algebras, to appear in Comm. Algebra.
Homological dimensions of crossed products, to appear in Glasgow Math. J.
Homological degrees of representations of categories with shift functors, to appear in Trans. Amer. Math. Soc.
On central stability, (withWL Gan), to appear in Bull. Lond. 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), preprint.
