Linyuan Lincoln Lu
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Education
| Ph.D. | Combinatorics | University of California, San Diego | 2002 |
| M.S. | Mathematics | University of Pennsylvania, Philadelphia | 1999 |
| M.S. | Computer Science | University of Pennsylvania, Philadelphia | 1999 |
| B.S. | Mathematics | Nankai University, Tianjin, China | 1991 |
Experience
| 2013 – Present | Professor | Department of Mathematics, Univ. of South Carolina |
| 2009 – 2012 | Associate Professor | Department of Mathematics, Univ. of South Carolina |
| 2004 – 2009 | Assistant Professor | Department of Mathematics, Univ. of South Carolina |
| 2002 – 2004 | Postdoc | University of California, San Diego |
Research
Research Interests
Large information networks, probabilistic methods, spectral graph theory, random graphs, extremal problems on hypergraphs and posets, algorithms, and graph theory.
Current Projects
- Turan problems on hypergraphs
- Random graphs/hypergraphs
- Spectral analysis on graphs/hypergraphs
- Extremal poset problems
- Ricci curvatures of graphs
- Probabilistic methods
- Other problems in graph theory
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Teaching Activities
Current Courses
- Math 142 - Calculus II
- Math 576 - Combinatorial Game Theory
Previous Courses
- 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 (HONORS)
- Math 374 - Discrete Structures
- Math 526 - Numerical linear algebra
- Math 550 - Vector Calculus
- Math 570 - Discrete optimization
- Math 574 - Discrete Mathematics I
- Math 576 - Combinatorial Game Theory
- Math 776 - Graph theory (I)
- Math 777 - Graph theory (II)
- Math 778E - Selected Topics: Extremal Graph Theory
- Math 778P - Selected topics in Discrete Mathematics (Probabil St Methds)
- Math 778S - Selected Topics: Spectral Graph Theory
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Honors and Other Special Scientific Recognition
- Receiving a prize of $100 from Ron Graham on December 8, 2008 for settling a twenty-years-old Erdos prized problem.
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Selected Publications
- Linyuan Lu and Xing Peng, The Fractional Chromatic Number of Triangle-free Graphs with 3, Discrete Mathematics 312, No. 24, (2012), 3502-3516.
- Jingfen Lan, Linyuan Lu, and Lingsheng Shi, Graphs with Diameter n-e Minimizing the Spectral Radius, Linear Algebra and its Application, 437, No.11, (2012), 2823-2850.
- Linyuan Lu and Xing Peng, Loose Laplacian spectra of random hypergraphs, Random Structures & Algorithms, 41 No. 4, (2012), 521-545.
- Linyuan Lu and Xing Peng, Monochromatic 4-term arithmetic progressions in 2-colorings of Zn, J. Combin. Theory Ser. A, 119 No. 5, (2012), 1048-1065.
- Andrew D. King, Linyuan Lu, and Xing Peng, A fractional analogue of Brook's theorem, SIAM J. Discrete Math., 26 (2012), 452-471.
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IMI Preprints and Seminars
IMI Preprints
- Diamond-free Families (2011)
- Using Lovász local lemma in the space of random injections (2006)
- On a problem of Erdős and Lovász on coloring non-uniform hypergraphs (2006)
- The volume of the giant component of a random graph with given expected degrees (2005)
- Concentration inequalities and martingale inequalities - a survey (2005)
IMI Seminars
- Turán Problems on Non-uniform Hypergraphs (2012)
- On crown-free families of subsets (2012)
- Ricci-flat graphs (2012)
- An exact result and its application on hypergraph Turan numbers (2008)
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