Welcome to Xizhi Liu's Home Page
Liu, Xizhi (刘西之)
Email: xizhi.liu.ac at gmail.com
I am currently a Research Fellow at
Mathematics Institute,
University of Warwick,
supervised by Prof. Oleg Pikhurko.
I got my Ph.D. in 2022 from
the Department of Mathematics, Statistics, and Computer Science,
University of Illinois at Chicago (UIC).
My advisor was Prof. Dhruv Mubayi.
I got my B.S. in 2018 from the
School of Mathematical Sciences,
University of Science and Technology of China (USTC).
My undergraduate advisor was Prof. Jie Ma.
Research Interests:
Extremal Combinatorics and related areas (Theoretical Computer Science, Complexity Theory, Discrete Geometry, etc.). Teaching:
01 Jan - 16 Mar. 2024,
MA9M2 Topics in Combinatorics, University of Warwick, (Instructor).
21-25 Aug 2023,
Minicourse on Extremal Hypergraph Theory, Suzhou University, (Instructor).
2022 Fall, Extremal Combinatorics (online Zoom), Fuzhou University , (Instructor).
2020 Spring, Math 165, Calculus for Business, UIC, (TA).
2019 Fall, Math 110, College Algebra, UIC, (TA).
2019 Spring, Math 310, Applied Linear Algebra, UIC, (TA).
2018 Fall, Math 310, Applied Linear Algebra, UIC, (TA).
Research:
Submitted
On a hypergraph Mantel theorem, 18pp. arXiv
A note on the minimum size of Turan systems, (with O. Pikhurko) 8pp. arXiv
Tiling H in dense graphs, (with N. Chen, L. Sun, and G. Wang) 45pp. Calculations file, arXiv
Density Hajnal-Szemeredi theorem for cliques of size four, (with J. Hou, C. Hu, and Y. Zhang) 99pp. Calculations file, arXiv
The Turan density of the tight 5-cycle minus one edge, (with L. Bodnar, J. Leon, and O. Pikhurko) 26pp. arXiv
Phase transition of degenerate Turan problems in p-norms, (with J. Gao, J. Ma, and O. Pikhurko) 28pp. arXiv
Positive codegree Andrasfai-Erdos-Sos theorem for the generalized triangle, (with S. Ren and J. Wang) 9pp. arXiv
Andrasfai-Erdos-Sos theorem for the generalized triangle, (with S. Ren and J. Wang) 23pp. arXiv
Generalized Andrasfai-Erdos-Sos theorems for odd cycles, (with Z. Chen, J. Hou, and C. Hu) 7pp. arXiv
Uniquely colorable hypergraphs, (with J. Ma, T. Wang, and T. Zhu) 29pp. arXiv
On the boundedness of degenerate hypergraphs, (with J. Hou, C. Hu, H. Li, C. Yang, and Y. Zhang) 19pp. arXiv
Nondegenerate Turan problems under (t,p)-norms, (with W. Chen, D. Ilkovi, J. Leon, and O. Pikhurko) 46pp.
Calculations file, arXiv
Tight bounds for rainbow partial F-tiling in edge-colored complete hypergraphs, (with J. Deng, J. Hou, and C. Yang) 19pp. arXiv
Strong stability from vertex-extendability and applications in generalized Turan problems, (with W. Chen) 30pp. arXiv
A generalized Turan extension of the Deza-Erdos-Frankl Theorem, (with C. Helliar) 12pp. arXiv
A criterion for Andrasfai--Erdos--Sos type theorems and applications, (with J. Hou and H. Zhao) 23pp. arXiv
Many vertex-disjoint even cycles of fixed length in a graph, (with J. Hou, C. Hu, H. Li, C. Yang, and Y. Zhang) 12pp. arXiv
A step towards a general density Corradi-Hajnal Theorem, (with J. Hou, H. Li, L.-T. Yuan, and Y. Zhang) 32pp. arXiv
Accepted (free open-access journal, Chinese math journal)
Random Turan and counting results for general position sets over finite fields, (with Y. Chen, J. Nie, and J. Zeng) Sci. China Math. (28pp). arXiv
Finite hypergraph families with rich extremal Turan constructions via mixing patterns, (with O. Pikhurko) Forum of Math, Sigma, (60pp). arXiv
Exact results for some extremal problems on expansions I, (with J. Song and L. Yuan), Commun. Math. Stat. (50pp), arXiv
Hypergraphs with many extremal configurations, (with D. Mubayi and C. Reiher) (34pp), Israel. J. Math., arXiv
Toward a density Corradi-Hajnal theorem for degenerate hypergraphs, (with J. Hou, C. Hu, H. Li, C. Yang, and Y. Zhang), J. Combin. Theory Ser. B 172 (2025), 221-262 (42pp). arXiv, journal
Hypergraph anti-Ramsey theorems, (with J. Song), J. Graph Theory, (9pp) arXiv, journal
A note on extremal constructions for the Erdos-Rademacher problem, (with O. Pikhurko), Combin. Probab. Comput. 34 (2025), no. 1, 52–62 (11pp),
arXiv, journal
Turan problems in pseudorandom graphs, (with D. Mubayi and David Munha Correia), Combin. Probab. Comput. 33 (2024), no. 5, 583–596 (14pp), arXiv, journal
Cancellative hypergraphs and Steiner triple systems, J. Combin. Theory Ser. B 167 (2024), 303-337 (35pp). arXiv, journal
Hypergraphs with infinitely many extremal constructions, (with J. Hou, H. Li, D. Mubayi, and Y. Zhang) Discrete Analysis 2023:18, 34 pp. arXiv,
journal
Hypergraph Turan densities can have arbitrarily large algebraic degree, (with O. Pikhurko) J. Combin. Theory Ser. B 161 (2023), 407-416 (10pp). arXiv,
journal
Stability theorems for some Kruskal-Katona type results, (with S. Mukherjee) European J. Combin. 110:103666, 2023, (20pp). arXiv,
journal
The feasible region of induced graphs, (with D. Mubayi and C. Reiher) J. Combin. Theory Ser. B 158 (2023), 105--135 (31pp). arXiv,
journal
A unified approach to hypergraph stability, (with D. Mubayi and C. Reiher) J. Combin. Theory Ser. B 158 (2023), 36--62 (27pp). arXiv,
journal
Tight query complexity bounds for learning graph partitions, (with S. Mukherjee) Conference on Learning Theory (COLT), 2022 (13pp). arXiv,
journal
Hypergraphs without non-trivial intersecting subgraphs, Combin. Probab. Comput. 31(6), 1076-1091, 2022 (16pp). arXiv,
journal
On explicit constructions of designs, (with D. Mubayi) Electron. J. Combin. 29 (2022), no. 1, Paper No. 1.53, (11pp). arXiv,
journal
Independent sets in hypergraphs omitting an intersection, (with T. Bohman and D. Mubayi) Random Structures Algorithms 61 (2022), no. 3, 493--519 (27pp). arXiv,
journal
On a generalized Erdos-Rademacher problem, (with D. Mubayi) J. Graph Theory 100 (2022), no. 1, 101--126 (26pp). arXiv,
journal
Sparse halves in K4-free graphs, (with J. Ma) J. Graph Theory 99 (2022), no. 1, 5–25 (21pp). arXiv,
journal
A hypergraph Turan problem with no stability, (with D. Mubayi) Combinatorica 42 (2022), no. 3, 433–462 (30pp). arXiv,
journal
Tight bounds for Katona's shadow intersection theorem, (with D. Mubayi)
European J. Combin., 97:103391, 2021, (17pp). arXiv,
journal
The feasible region of hypergraphs, (with D. Mubayi) J. Combin. Theory Ser. B 148 (2021), 23--59 (37pp). arXiv,
journal
New short proofs to some stability theorems, European J. Combin., 96:103350, 2021, (8pp).
arXiv, journal
Structural results for conditionally intersecting families and some applications,
Electron. J. Combin., 33(2), 2020, (13pp).
arXiv, journal
d-cluster-free sets with a given matching number, European J. Combin., 82:103000, 2019, (19pp). arXiv,
journal
Thesis
Extremal Hypergraph Problems
(contains some unpublished results and shorter proofs to some published results).