Department of Mathematics, Shanghai University, Shanghai, China

Email: nangao@shu.edu.cn

Homepage: https://www.scicol.shu.edu.cn/szdw/faculty/gn.htm

**Academic employment**

1. March, 2018--present, Professor, Department of Mathematics, College of Science, Shanghai University, China.

2. March, 2011--February, 2018, Associate professor, Department of Mathematics, College of Science, Shanghai University, China.

3. July, 2008--February, 2011, Lecturer, Department of Mathematics, College of Science, Shanghai University, China.

**Education**

September, 2005鈥擩une, 2008, Ph.D., Department of Mathematics, Shanghai Jiaotong University. Supervisor: Pu Zhang.

**Research Interests**

1. Representation Theory of Algebras

2. Triangulated categories

3. Gorenstein homology algebra

**Research Projects**

1. 2018-2021, the National Natural Science Foundation of China, title: Representation and homology theory of Morita algebra. Project Director.

2. 2012-2014, the National Natural Science Foundation of China, title: Recollements and Gorenstein derived categories. Project Director.

3. 2010, the National Natural Science Foundation of China, title: Research on Gorenstein derived categories and construction of Gorenstein projective modules. Project Director.

4. Key subspecialty project of Pudong New Area Health Commission, title: the utility of topological matrix group algorithm in lung nodule detection. Co-head.

**Selected Published SCI Papers (2008-Present)**

1 **N.Gao**, J.Ma, X.Y.Liu, RSS equivalence over a class of Morita ring, J.Algebra 573(2021), 336-363.

2 **N.Gao**, S.Koenig, C.Psaroudakis, Ladders of recollements of abelian categories, J. Algebra 579(2021), 256-302.

3 Y.J.Wang, **N.Gao**锛�Some properties for almost cellular algebras, Electronic Research Archive 29(1)(2021), 1681-1689.

4 **N.Gao**, W.H.Zhao, Singular equivalences arising from Morita rings, Ark. Mat. 58(2020), 87鈥�94.

5 **N.Gao**, S. Koenig, C.Psaroudakis, Recollements of abelian categories and ideals in heredity chains鈥揳 recursive approach to quasi-hereditary algebras, Proc. Amer. Math. Soc. 147 (2019), 4625-4637.

6 **N.Gao**, C.Psaroudakis, Ladders of compactly generated triangulated categories and preprojective algebras, Applied Categorical Structures 26(4)(2018), 657-679.

7 M.T.Liu, R.X.Li, **N.Gao**, Morphism categories of Gorenstein-projective modules, Algebra Colloq. 25(3)(2018), 377-386.

8 R.X.Li, M.T.Liu, **N.Gao**, Algebraic K-theory of Gorenstein projective modules, Front. Math. China 13(1)(2018), 55-66.

9 **N.Gao**, X.J.Xu, Homological epimorphisms, compactly generated t-structures and Gorenstein-projective modules, Chin. Ann. Math. 39B(1)( 2018), 47-58.

10 **N.Gao**, C.Psaroudakis, Gorenstein homological aspects of monomorphism categories via Morita rings, Algebra Represent. Theory 20(2)(2017), 487-529.

11 **N.Gao**, Y.Q.Yin, P.Zhang, Comparisons of left recollements, Algebra Represent. Theory 20(3) (2017), 659-673.

12 **N.Gao**, Gorensteinness, homological invariants and Gorenstein derived categories, Sci. China Math. 60(3) (2017), 431-438.

13 **N.Gao**, S.Koenig, Double centraliser property and morphism categories, Proc. Amer. Math. Soc. 144(3)(2016), 971-981.14 Y.Q.Yin, N.Gao, Upper recollements and triangle expansions, Acta Math. Sin. (Engl. Ser.) 32(2016), 1323-1336.

15 **N.Gao**, K.Q.Hao, Extension closure of glueing t-structures, (Chinese) Commun. Appl. Math. Comput. 30 (2016), 364-368.

16 **N.Gao**, S.Koenig, Grade, dominant dimension and Gorenstein algebras, J. Algebra 427(2015), 118-141.

17 **N.Gao**, A smashing subcategory of the homotopy category of Gorenstein projective modules, Applied Categorical Structures 23(2015), 87-91.

18 **N.Gao**, On homotopy categories of Gorenstein modules: compact generation and dimensions, Homology, Homotopy and Applications 17(2)(2015), 13-24.

19 W.W.Chang, **N. Gao**, (n,m)-strongly 尉-Gorenstein projective objects in triangulated categories, (Chinese) Commun. Appl. Math. Comput. 28 (2014), 166-174.

20 **N.Gao**, Hopf extensions of CM-finite Artin algebras, Algebra Represent. Theory 16(3)(2013), 605-613.

21 **N.Gao**, L.F.Song, Contravariant finiteness of modules of Gorenstein projective dimension鈮�I, Far East J. Math. Sci. (FJMS) 68 (2012), 153-160.

22 **N.Gao**, Recollements of Gorenstein derived categories, Proc. Amer. Math. Soc. 140(1)(2012), 147-152.

23 **N.Gao**, Auslander-Reiten triangles on Gorenstein derived categories, Comm. Algebra 40(10)(2012), 3912-3919.

24 **N.Gao**, Stable t-structures and homotopy category of Gorenstein-projective modules, J. Algebra 324(9)(2010), 2503-2511.

25 **N.Gao**, P.Zhang, Gorenstein derived categories, J. Algebra 323(2010), 2041-2057.

26 **N.Gao**, P.Zhang, Strongly Gorenstein projective modules over triangular matrix Artin algebras, Comm. Algebra 12(2009), 4259-4268.

27 **N.Gao**, The relative transpose over Cohen-Macaulay finite Artin algebras, Chin. Ann. Math. 30B(3)(2009), 231-238.

28 **N.Gao**, Symmetries in Yetter-Drinfeld categories over weak Hopf algebras, Acta.Math.Sci. 28B(4)(2008), 870-876.

29 **N.Gao**, Actions of semisimple weak Hopf algebras. J. Math. Res. Exposition 28 (2008), 25-34.

**Invited Talk/ Colloquia**

1. (Colloquia) Ladders of recollements of abelian categories, East China Normal University, October 29, 2021.

2. (Colloquia) Relative rigid modules and Gorenstein silting module, Northeast Normal University, October 28, 2021.

3. (Colloquia) Silting properties via abelian ladders, Sichuan University, October 22, 2021.

4. (Invited Talk) A series of online reports and discussions on cell algebras and quiver algebras, Beijing Union University, China, July, 13-14, 2021.

5. (Invited Talk) The 6th national seminar on rings and algebras, Sichuan University of Arts and Science, China, June, 26-27, 2021.

6. (Invited Talk) 2021 Wuhan algebra seminar, Jianghan University, China, June, 5-6, 2021.

7. (Colloquia) RSS equivalences over a class of Morita rings, Huaqiao University, May 21, 2021.

8. (Colloquia) Gorenstein derived categories and related topic, Capital Normal University, May 17, 2021.

9. (Invited Talk) 2020 Symposium on frontier progress and Prospect of group and algebraic representation, Shanghai Jiaotong University, China, June, 6-7, 2020.

10. (Invited Talk) The 8th China-Japan-Korea International Symposium on Ring Theory, Nagoya University, Japan, August, 26-31, 2019.

11. (Invited Talk) Asia-Australia Algebra Conference, Western Sydney University, Australia, January, 21-25, 2019.

12. (Invited Talk) The 4th Yangtze River Delta algebra Conference, Shanghai jiaotong University, China, October, 26-28, 2018.

13. (Invited Talk) 2017 Academic Annual Meeting of China Mathematics Society, Xiangtan University, China, October, 20-24, 2017.

14. (Invited Talk) The 14th National Conference on algebra, Yangzhou University, China, May, 26-31, 2016.

15. (Invited Talk) 2015 Yangtze River Delta algebra Conference, Anhui University, China, October 20--November 2, 2015.

**Awards**

1 The third prize of Professor group in the first Shanghai University teacher teaching innovation competition, 2020.

2. National first-class undergraduate courses, 2020.

3. 2017-2018 "March 8th Red Banner pacesetter " of Shanghai University.

4. the third prize of Shanghai Natural Science and technology progress award (4th).

5 The first prize of Shanghai municipal teaching achievement (9th).

**Services**

1 Mathematical Review in American Mathematical Society;

2 The Fourth Board of directors of the Chinese Higher Education Association鈥檚 Specialized Committee for Education Mathematics;

3 Review expert of the National Natural Science Foundation of China;

4 Communication expert of the degree center of the Ministry of education;

5 Expert of Shanghai Science and technology experts database.