Research Areas

Geometry and Analysis on graphs

Educational Background

1981-1985, Bachelor, Fujian Normal University, China

1994-1997, Ph.D, University of Jyvaskyla, Finland

Work Experience

Appointments:

01/2019- present, Professor, Yau Mathematical Science Center/Department of Mathematics, Tsinghua University, Beijing, China

07/2002-present, Professor of Mathematics, Renmin University of China, Beijing , China

05/1998-06/2002, Associate Professor, Renmin University of China, Beijing, China

09/1997-04/1998, Research Fellow, University of Jyvaskyla, Finland

07/1998-08/1994, Lecturer, Fujian Normal University

Visiting:

01/2018-02/2018, Visiting Follow, Department of Mathematics, Harvard University ,USA

01/2017-03/2017, Visiting Follow, Department of Mathematics, Harvard University, USA

07/2016, Visiting Follow, Department of Mathematics, University of Bielefeld, Germany

02/2016-03/2016, Visiting Follow, Department of Mathematics, Harvard University, USA

02/2015-05/2015, Visiting Follow, Department of Mathematics, Harvard University, USA

04/2014-06/2014, Visiting Follow, Department of Mathematics, Taiwan University

01/2013-05/2013, Visiting Follow, Department of Mathematics, Harvard University, USA

07/2012-08/2012, Visiting Follow, Department of Mathematics, University of Bielefeld, Germany

01/2012-02/2012, Visiting Follow, Department of Mathematics, Chinese University of Hong Kong

09/2009-09/2010, Visiting Follow, Department of Mathematics, Harvard University, USA

09/2004-06/2005, Visiting Follow and Post-doctor, Department of Mathematics, Harvard University, USA

Publish one’s thesis

Preprint:

1. Alexander Grigor'yan, Yong Lin, Yuri Muranov, Shing-Tung Yau, Homologies of path complexes and digraphs, preprint.

2. Chao Gong, Yong Lin, Shuang Liu, CDE' Inequalities on Graphs with Unbounded Laplacians, preprint.

3. BoboHua, Yong Lin, Yanhui Su, Payne-Polya-Weinberger, Hile-Protter and Yang’s inequalities for Dirichlet Laplace eigenvalues on integer lattices, preprint.

4. Paul Horn, Yong Lin, Shing-Tung Yau, Variational inequalities on graphs, preprint.

5. Shuliang Bai, Yong Lin, Linyuan Lu, Zhiyu Wang, Shing-Tung Yau, Discovering hierarchical structures in weighted graphs using Ricci-flow method, preprint.

6. Alexander Grigor'yan, Yong Lin, Shing-Tung Yau, Reidemeister torsion and analytic torsion of graph, preprint.

7. Yong Lin, Yuanyuan Xie, The existence of the solution of the wave equation on graph, preprint.

8. Yong Lin, Yuanyuan Xie, Semilinear heat equations and parabolic variational inequalities on graphs, preprint.

9. Yong Lin, Chong Wang, Witten-Morse functions and Morse inequalities on digraphs, preprint.

Publications:

1. Yong Lin, Chong Wang, Shing-Tung Yau, Discrete Morse theory on digraphs, to appear in Pure and Applied Mathematics Quarterly.

2. Yong Lin, Yun Yan Yang , Calculus of variations on locally finite graphs, to appear in Revista Matemática Complutense.

3. Yong Lin, Yun Yan Yang, A heat flow for the mean field equation on a finite graph, Calculus of Variations and Partial Differential Equations, 60:206, 2021.

4. Yong Lin, Sze-Man Ngai, Shing-Tung Yau, Heat kernels on forms defined on a subgraph of a complete graph, Mathematische Annalen , 380, 1891–1931, 2021.

5. An Huang, Yong Lin, Shing-Tung Yau, Existence of Solutions to Mean Field Equations on Graphs, Communications in Mathematical Physics, 377, 613-621, 2020.

6. Alexander Grigor'yan, Yong Lin, Yuri Muranov, Shing-Tung Yau, Path complexes and their homologies, Journal of Mathematical Science, 248(5), 564-599, 2020.

7. Pual Horn, Yong Lin, Shuang Liu, Shing-Tung Yau, Volume doubling, Poincar\'{e} inequality and Guassian heat kernel estimate for nonnegative curvature graphs, Journal für die reine und angewandte Mathematik(Crelle's journal), 757, 89-130, 2019.

8. Bobo Hua, Yong Lin, Graphs with large girth and nonnegative curvature dimension condition, Communications in Analysis and Geometry, 27(3), 619-639, 2019.

9. Chao Gong, Yong Lin, Shuang Liu, Shing-Tung Yau, Li-Yau inequality for unbounded Laplacian on graphs, Advances in Mathematics, 357, 2019.

10. Lin,Yong, Liu,Shuang, Song,Hongye, Ultracontractivity and Functional Inequalities on Infinite Graphs, Discrete & Computational Geometry, 61(1), 198-211, 2019.

11. Lin,Yong, Wu,Yiting, Blow-up problems for nonlinear paraboliv equations on locally finite graphs, Acta Mathematica Scientia, 38(3), 843-856,2018.

12. Lin,Yong, Song,Hongye, Harnavk and mean value inequalities on graphs, Acta Mathematica Scientia, 38(6), 1751-1758, 2018.

13. Yong Lin, Shuang Liu, Hongye Song, Log-Sobolev Inequalities on Graphs with Positive Curvature, Mathematical Physics and Computer Simulation, Volume 40(3), 2017.

14. Chao Gong, Yong Lin, Equivalent Properties for CD Inequalities on Graphs with Unbounded Laplacians, Chinese Annals of Mathematics, Series B, Volume 38(5), 1059-1070, 2017.

15. Yong Lin, Yiting Wu, On-diagonal lower estimate of heat kernels on graphs, Journal of Mathematical Analysis and Applications, Volume 456(2), 1040-1048, 2017.

16. Yong Lin, Yiting Wu, The existence and nonexistence of global solutions for a semilinear heat equation on graphs, Calculus of Variations and Partial Differential Equations, Volume 56(4), 2017.

17. Alexander Grigor'yan, Yong Lin, Yun Yan Yang, Existence of positive solutions to some nonlinear equations on locally finite graphs, Science China Math., Vol.60, 1311-1324, 2017.

18. Bobo Hua, Yong Lin, Stochastic completeness for graphs with curvature dimension conditions, Advances in Mathematics, 306, 279–302, 2017.

19. Yong Lin, Shuang Liu, Yun Yan Yang, A Gradient Estimate for Positive Functions on Graphs, Journal of Geometric Analysis, Volume 27, 1667-1679, 2017.

20. Frank Bauer, Fan Chung, Yong Lin, Yuan Liu, Curvature Aspects of Graphs, Proceedings of the American Mathematical society, Volume 145, 2033-2042, 2017.

21. Alexander Grigor'yan, Yong Lin, Yun Yan Yang, Yamabe type equations on graphs, Journal of Differential Equations, Volume 261, Number. 9, 4924-4943, 2016.

22. Alexander Grigor'yan, Yong Lin, Yun Yan Yang, Kazdan-Warner equation on graph, Calculus of Variations and Partial Differential Equations, Volume 55, Number 4, 2016.

23. Yong Lin, Shuang Liu, Yun Yan Yang, Global gradient estimate on graph and its application, Acta Mathematica Sinica,Volume 32, Number 11, 1350-1356, 2016.

24. Zu-Guo Yu, Huan Zhang, Da-Wen Huang, Yong Lin, Vo Anh, Multifractality and Laplace spectrum of horizontal visibility graphs constructed from fractional Brownian motion, Journal of Statistical Mechanics, 3, 2016.

25. Alexander Grigor'yan, Yong Lin, Yuri Muranov, Shing-Tung Yau,, Cohomology of digraphs and (undirected) graphs, Asian Journal of Mathematics, Volume19, Number5, 2015.

26. Frank Bauer, Paul Horn, Yong Lin, Gabor Lippner, Dan Mangoubi, Shing-Tung Yau, Li-Yau inequality on graphs, Journal of Differential Geometry, 99, 359-405, 2015.

27. Alexander Grigor'yan, Yong Lin, Yuri Muranov, Shing-Tung Yau, Homotopy theory of digraphs, Pure and Applied Mathematics Quarterly, Volume 10, Number 4, 619-674, 2014.

28. Yong Lin, Linyuan Lu and Shing-Tung Yau, Ricci-flat graphs with girth at least five, Communications in Analysis and Geometry, Volume 22, Number 4, 1–17, 2014

29. Fan Chung, Yong Lin and Shing-Tung Yau, Harnack inequalities for graphs with non-negative Ricci curvature, Journal of Mathematical Analysis and Applications, Vol.415, Issue 1, 25-32, 2014.

30. Yong Lin, Ricci curvature and functional inequalities on graphs, Fifth International Congress of Chinese Mathematicians. Part 1, 2, 663–675, AMS/IP Stud. Adv. Math., 51, pt. 1, 2, Amer. Math. Soc., Providence, RI, 2012.

31．Yong Lin, Gapor Lippner, Shing-Tung Yau, Quantum tunneling on graphs, Communications in Mathematical Physics, Vol.311, no. 1, 113-132, 2012.

32. Yong Lin, Linyuan Lu and Shing-Tung Yau, Ricci curvature of graphs, Tohoku Mathematical Journal, Vol.63, no.4, 605-627, 2011.

33. Yong Lin and Shing-Tung Yau, Ricci curvature and eigenvalue estimate on locally finite graphs, Mathematical Research Letter, Vol.17, No.2, 345-358, 2010.

34. Yong Lin, Gapor Lippner, Dan Mangaubi, Shing-Tung Yau, Nodal Geometry of graphs on Surfaces, Discrete and Continuous Dynamical System, Vol.28, No.3, 1291-1298, 2010.

35. Yong Lin and Lifeng Xi, Lipschitz Continuity of Harmonic Function on Graphs, Journal of Mathematical Analysis and Applications, Vol.366, Issue 2, 673-679, 2010.

36. Yong Lin and Huojun Ruan, Maximal functions and Fourier transforms of self-similar measures, Chaos,Solitons and Fractals,Vol. 27，2006.

37. Dachun Yang and Yong Lin, Spaces of Lipschitz type on metric spaces and their applications, Proc. Edinb. Math. Soc(2) 47, no.3. 709—752,2004.

38. Hua Su and Lin Yong, R\S analysis of Chinese securities market, Tsinghua Sci. Technol., Vol8, No. 5, 2003.

39. Yong Lin and Lifeng Xi, Whitney's Critical Set in Fractal, Chaos, Solitons and Fractals, Vol.14, 2002.

40. Yong Lin and Pertti Mattila, Menger curvature and C1 regularity of fractals, Proceeding of American Mathematics Society, Vol.6, 2001.

41. Yong Lin, Menger curvature, singular integrals and analytic capacity, Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes 111, 1997.

42. Yong Lin, Meromorphic solutions to six classes of classical nonlinear ordinary differential equations. I., Acta Math. Sci.(Chinese), Vol.12, No. 3, 1992.

43. Yuzan He and Yong Lin, On factorization of meromorphic functions satisfying nonlinear ordinary differential equations, International Symposium in memory of Hua Loo Keng, Vol. II (Beijing), 123-133, Springer, 1991