# Department of **Mathematics**

## Directory

## Linyuan Lu

Title: |
Professor |

Department: |
Mathematics College of Arts and Sciences |

Email: |
lu@math.sc.edu |

Phone: |
803-777-4154 |

Office: |
LeConte 403 LeConte 419A (Chair's Office) |

Resources: |
My Website Curriculum Vitae [PDF] |

### 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.