Research Interests

Dr. Lu is well-known nationally and internationally for his research work on large information networks, sparse random graphs, probabilistic methods, extremal problems on hypergraphs and posets, spectral graph/hypergraph theory, Ramsey type problems, Discrete Geometry, and other problems in graph theory. He has published 1 book, 2 book chapters, 70 Journal papers, and 13 conference papers. He was invited to give lecture series internationally four times, twelve 45-minutes talks at national and international conferences, and twenty-seven colloquium/seminar talks at other universities, and forty-eight 25-minute talks at various conferences and workshops. Furthermore, he has been supported by 6 NSF grants and 2 ONR grants. According to Google Scholar, Dr. Lu has 9599 citations with h-index 29 and i10-index 58. He had solved a $100-prized Erdos problem.

Education

• Ph.D. in Combinatorics, University of California, San Diego (2002)
• M.S. in Mathematics, University of Pennsylvania (1999)
• M.S. in Computer Science, University of Pennsylvania (1999)
• B.S. in Mathematics, Nankai University, Tianjin, China (1991)

Experience

• Department Chair, University of South Carolina (2018 – present)
• Professor, University of South Carolina (2013 – present)
• Associate Professor, University of South Carolina, (2009 – 2013)
• Assistant Professor, University of South Carolina, (2004 – 2009)
• Postdoc, University of California, San Diego (2002 – 2004)

Courses Taught

• MATH 141: Calculus I
• MATH 142: Calculus II
• MATH 198: Introduction to Careers and Research in the Mathematical Sciences
• MATH 241: Vector Calculus
• MATH 242: Elementary Differential Equations
• MATH 374: Discrete Structures
• MATH 526: Numerical Linear Algebra
• MATH 570: Discrete Optimization
• MATH 574: Discrete Mathematics
• MATH 576: Combinatorial Game Theory
• MATH 776: Graph Theory I
• MATH 777: Graph Theory II
• MATH 778: Topic Courses in Discrete Mathematics
• Probabilistic Methods
• Spectral Graph Theory
• Large Networks and Graph Limits
• Extreme Graph Theory

Selected Publications

Books and book chapters

• Fan Chung and Linyuan Lu, Complex graphs and networks, CBMS Regional Conference Series in Mathematics; number 107, (2006), 264+vii pages. ISBN-10: 0-8218-3657-9, ISBN-13: 978-0-8218-3657-6.
• Linyuan Lu,  Austin Mohr, and Laszlo Szekely, Quest for Negative Dependency Graphs, in Recent Advances in Harmonic Analysis and Applications: In Honor of Konstantin Oskolkov (Eds. D. Bilyk, L. DeCarli, A. Petukhov, A. M. Stokolos, B. D. Wick), Springer Proceedings in Mathematics & Statistics, (2012) 243-258.
• William Aiello, Fan Chung, and Linyuan Lu. Random evolution in massive graphs, in Handbook on Massive Data Sets, (Eds. James Abello et al.), (2002) 97–122.

Recent Journal papers

• Linyuan Lu, Matthew H.Y. Xie, Arthur L.B. Yang, Kazhdan-Lusztig polynomials of fan matroids, wheel matroids and whirl matroids, Journal of Combinatorial Theory, Series A 192, November 2022, 105665
• Mark Ellingham, Linyuan Lu,  Zhiyu Wang,  Maximum spectral radius of outerplanar 3-uniform hypergraphs, Journal of Graph Theory, 100, Issue 4, (2022), pp 671-685.
• Linyuan Lu and Jushua Thompson, Poset Ramsey Numbers for Boolean Lattices, Order, 39 (2022), 171–185.
• Shuliang Bai and Linyuan Lu, Turán Density of 2-Edge-Colored Bipartite Graphs with Application on {2,3}-Hypergraphs, The Electronic Journal of Combinatorics, 28 Issue 3 (2021), P3.42. 
• Linyuan Lu and Zhiyu Wang,  On the cover Turán number of Berge hypergraphs, European Journal of Combinatorics, 98, December 2021, 103416.
• Linyuan Lu and  Zhiyu Wang, On Hamiltonian Berge cycles in [3]-uniform hypergraphs, Discrete Mathematics 344, Issue 8, August 2021, 112462
• David Cushing, Riikka Kangaslampi, Yong Lin, Shiping Liu, Linyuan Lu, Shing-Tung Yau,Ricci-flat cubic graphs with girth five, Communications in Analysis and Geometry, 29 (7)  (2021), 1559 – 1570.
• Alice L. L. Gao, Linyuan Lu, Matthew H. Y. Xie, Arthur L. B. Yang, Philip B. Zhang, The Kazhdan-Lusztig polynomials of uniform matroids, Advances in Applied Mathematics, 122 (2021), 102117.
• Liying Kang, Lele Liu, Linyuan Lu, Zhiyu Wang, The extremal p-spectral radius of Berge- hypergraphs, Linear Algebra and its Applications, 610, (2021) 608-624.
• Linyuan Lu and Zhiyu Wang, Anti-Ramsey Number of Edge-Disjoint Rainbow Spanning Trees, SIAM J. Discrete Math., 34(4), (2020) 2346-2362.
• Linyuan Lu and Zhiyu Wang, On the cover Ramsey number of Berge hypergraphs, Discrete Mathematics, 343(9), (2020), 111972.
• Mohammad Ali Javidian, Linyuan Lu, Marco Valtorta, Zhiyu Wang, On a hypergraph probabilistic graphical model, Annals of Mathematics and Articial Intelligence  88 (2020), 1003-1033.
• Lele Liu and Linyuan Lu, The α-normal labeling method for computing the p-spectral radii of uniform hypergraphs, Linear and Multilinear Algebra, published online on May 2020.
• Shuliang Bai and Linyuan Lu, Spectral radius of {0, 1}-tensor with prescribed number of ones, Linear Algebra Appl. 558 (2018), 205-235.
• Linyuan Lu and Zhiyu Wang, On the size-Ramsey number of tight paths. SIAM J. Discrete Math. 32 (2018), no. 3, 2172-2179.
  Shuliang Bai and Linyuan Lu, A Bound on the Spectral Radius of Hypergraphs with e Edges, Linear Algebra Appl., 549, (2018), 203-218.