Xizhi Liu

Special-Term Professor, 2025–2031, School of Mathematical Sciences, University of Science and Technology of China

Email: liuxizhi at ustc dot edu dot cn (both my UIC and Warwick email accounts have expired)

Group Member

Wanfang Chen, Postdoc, July 2025–July 2027

Teaching

2026 Fall, MATH1009 线性代数(B1), USTC.
2026 Fall, FS1001 “科学与社会”研讨课, USTC.
2026 Summer, MATH4003 数学前沿课程 (1/5), USTC.
2026 Spring, MATH7425P 图论选讲 (2/4), USTC.
2025 Fall, MATH5006P 图论, USTC.
Apr. 15–19, 2025, Mini-course on hypergraph Turan problems , Taiyuan University of Technology.
Jan. 1–Mar. 16, 2025, MA9M2 Topics in Combinatorics , University of Warwick.
Aug. 21–25, 2023, Mini-course on Extremal Hypergraph Theory , Suzhou University.
2022 Fall, Extremal Combinatorics (online), Fuzhou University.

Conference / Workshop Organization

Jan. 14–17, 2026, 中科大冬季组合图论研讨会.
July 8–11, 2025, Combinatorics and Graph Theory Workshop, USTC.

Publications/Preprints/Research Notes ([arXiv], [GitHub:UnpolishedNotes], [GitHub:ResearchNotes])

Preprints/Research Notes (Some are preliminary drafts and have not yet been fully polished or verified by a human; some research notes are not intended for publication)

On the spectrum of minimum ℓ-degree Turan densities, (with H. Li) 28 pp.Scripts [GitHub]
Turing universality, computability, and incompleteness in hypergraph Turan theory, (with H. Li) 141 pp.[GitHub]
A finite family with transcendental uniform Turan density, (with H. Li) 36 pp.Scripts [GitHub]
Undecidability in uniform Turan densities, (with H. Li) 26 pp.[GitHub]
Gaps between Turan densities for r-graphs on r+1 vertices, (with H. Li) 17 pp.[GitHub]
On the VC-dimension of Erdos-Renyi random graphs, (with H. Li) 51 pp.[GitHub]
Tight Hamiltonian cycles in uniformly dense 3-graphs, (with Y. Chen and J. Han) 43 pp.[arXiv]
Forcing quasirandomness via rooted F-densities, (with H. Li) 21 pp.[arXiv]
Intervals of uniform Turan densities, (with H. Li and O. Pikhurko) 19 pp.[arXiv]
Transcendence and undecidability for ℓ-degree Turan densities, (with H. Li) 46 pp.[GitHub]
Transcendence and undecidability in hypergraph Turan densities, (with H. Li and H. Liu) 48 pp.[GitHub]
Nearly sharp bounds for lattice coverings by convex bodies, (with H. Li) 45 pp.[arXiv]
Accompanying draft: Two-stage binary correction for nearly linear lattice coverings, (with H. Li) 15 pp.[GitHub]
The density Hajnal-Szemeredi theorem, (with ***) 46 pp.[GitHub]
The anti-supersaturation problem, (with H. Li and J. Zeng) 21 pp.[GitHub]
Strong counterexamples to Mubayi's supersaturation conjecture in every uniformity, (with H. Li, H. Liu, and J. Wang) 27 pp.[arXiv]
Sharp bounds for minimal dependencies of linear-form powers, (with H. Li) 20 pp.[GitHub][arXiv]
Turan numbers of 4-uniform tight even cycles minus one edge, (with W. Chen, J. Hou, Y. Zhang, and H. Zhao) 24 pp.Scripts [arXiv]
A note on Bukh's construction of extremal graphs without small bicliques, (with H. Li) 11 pp.[GitHub]
Logarithmic colourings, monomial shrinking targets, and product-configuration obstructions, (with H. Li) 29 pp.[GitHub]
Exact extremal constructions for the inducibility of blowup graphs, (with W. Chen) 14 pp.[arXiv]
Physical-space scarring in generic Bunimovich stadia, (with H. Li) 15 pp.[arXiv]
Vertex-colored Turan theorems with applications in extremal hypergraph problems, (with W. Chen, J. Deng, J. Hou, and Y. Zhang) 34 pp.Scripts [arXiv]
Upper bounds on Turan densities via extremal set theory, (with Y. Chen, N. Yang, and T. Zhu) 14 pp.[arXiv]
The inducibility of 6-vertex graphs, (with L. Bodnar, J. Gao, J. Leon, O. Pikhurko, and S. Sun) 34 pp.Scripts [arXiv]
The spectral inducibility of graphs, (with L. Kang and Y. Lu) 14 pp.[arXiv]
A finite-board reduction for the Erdos matching conjecture and the 4-uniform case via exact certificates, (with J. Hou and C. Hu) 28 pp.Scripts [arXiv]
Intervals of hypergraph Turan densities, (with O. Pikhurko) 23 pp.[arXiv]
On Mubayi's polynomial-ideal conjecture and a hypergraph Turan theorem, (with H. Li) 13 pp.[arXiv]
A single 3-graph with infinite stability number, (with H. Li) 11 pp.[arXiv]
The spectral radius of k-chromatic r-graphs, (with J. Luo) 41 pp.[arXiv]
The number 4/9 is a non-jump for 3-graphs, (with D. Mubayi) 12 pp.[arXiv]
Spectral sensitivity of directed weighted networks: Why weakening edges may trigger synchronization, (with X. Wu, C. Zhang, T. Chen, and W. Lu) 18 pp.Scripts [arXiv]
A note on the t-partite link problem of Furedi, (with J. Hou, X. Hou, J. Zeng, and Y. Zhang) 14 pp.[arXiv]
This paper improves upon the following earlier research note: Improved upper bound for the Turan density of daisies, (with J. Hou and Y. Zhang) 10 pp.[GitHub]
The inducibility of Turan graphs, (with J. Ma and T. Zhu) 32 pp.[arXiv]
Andrasfai-Erdos-Sos theorem under max-degree constraints, (with S. Ren and J. Wang) 12 pp.[arXiv]
Tetrahedron conjecture in the ℓ₂-norm, (with L. Bodnar, W. Chen, J. Deng, J. Hou, J. Song, J. Yang, and Y. Zhang) 28 pp.Scripts [arXiv]
Odd hypergraph Mantel theorems, (with J. Hou, Y. Zhang, and H. Zhao) 13 pp.Scripts [arXiv]
Toward a rainbow Corradi-Hajnal theorem I, (with J. Deng, J. Hou, and C. Hu) 28 pp.[arXiv]
Spectral generalized Turan problems, 24 pp.[arXiv]
Exact Turan number of the Fano plane in the ℓ₂-norm, (with J. Hou and Y. Zhang) 43 pp.[arXiv]
Turan density of tight cycles minus one edge in the ℓ₂-norm, (with L. Bodnar, J. Deng, J. Hou, and H. Zhao) 18 pp.Scripts [arXiv]
The Turan density of short tight cycles, (with L. Bodnar, J. Leon, and O. Pikhurko) 28 pp.Scripts [arXiv]
On a hypergraph Mantel theorem, 18 pp.[arXiv]
Tiling H in dense graphs, (with N. Chen, L. Sun, and G. Wang) 45 pp.Scripts [arXiv]
Density Hajnal-Szemeredi theorem for cliques of size four, (with J. Hou, C. Hu, and Y. Zhang) 99 pp.Scripts [arXiv]
The Turan density of the tight 5-cycle minus one edge, (with L. Bodnar, J. Leon, and O. Pikhurko) 26 pp.Scripts [arXiv]
Andrasfai-Erdos-Sos theorem for the generalized triangle, (with S. Ren and J. Wang) 23 pp.[arXiv]
Uniquely colorable hypergraphs, (with J. Ma, T. Wang, and T. Zhu) 29 pp.[arXiv]
Nondegenerate Turan problems under (t,p)-norms, (with W. Chen, D. Ilkovi, J. Leon, and O. Pikhurko) 46 pp.Scripts [arXiv]
Strong stability from vertex-extendability and applications in generalized Turan problems, (with W. Chen) 30 pp.[arXiv]

Published/Accepted (Free open-access journal, Chinese math journal)

Covering large-dimensional Euclidean spaces by random translates of a given convex body, (with B. Bukh, J. Gao, O. Pikhurko, and S. Sun) Discrete Comput. Geom., 16 pp.[arXiv]
Generalized Andrasfai-Erdos-Sos theorems for odd cycles, (with Z. Chen, J. Hou, and C. Hu) Acta Math. Appl. Sin. Engl. Ser. 7 pp.[arXiv][journal]
A generalized Turan extension of the Deza-Erdos-Frankl theorem, (with C. Helliar) J. Graph Theory, 12 pp.[arXiv][journal]
A criterion for Andrasfai--Erdos--Sos type theorems and applications, (with J. Hou and H. Zhao) Ann. Appl. Math. 23 pp.[arXiv][journal]
On a refinement of the Ahlswede--Katona theorem, (with J. Hou and Y. Zhang) Ann. Appl. Math. 25 pp.Scripts [arXiv][journal]
Positive codegree Andrasfai-Erdos-Sos theorem for the generalized triangle, (with S. Ren and J. Wang) J. Graph Theory, 9 pp.[arXiv][journal]
Many vertex-disjoint even cycles of fixed length in a graph, (with J. Hou, C. Hu, H. Li, C. Yang, and Y. Zhang) J. Graph Theory, 12 pp.[arXiv][journal]
Convergence of spectra of digraph limits, (with J. Grebik, D. Kral, O. Pikhurko, and J. Slipantschuk) European J. Combin. 15 pp.[arXiv][journal]
A note on the minimum size of Turan systems, (with O. Pikhurko) Electron. J. Combin. 8 pp.[arXiv][journal]
Sabotage the Mantel theorem, (with N. Behague and D. Chakraborti) Electron. J. Combin. 8 pp.[arXiv][journal]
New upper bound for lattice covering by spheres, (with J. Gao, O. Pikhurko, and S. Sun) Mathematika, 15 pp.[arXiv][journal]
On the boundedness of degenerate hypergraphs, (with J. Hou, C. Hu, H. Li, C. Yang, and Y. Zhang) Acta Math. Sin. (Engl. Ser.) 19 pp.[arXiv][journal]
Tight bounds for rainbow partial F-tiling in edge-colored complete hypergraphs, (with J. Deng, J. Hou, and C. Yang) J. Graph Theory, 19 pp.[arXiv][journal]
Phase transition of degenerate Turan problems in p-norms, (with J. Gao, J. Ma, and O. Pikhurko) SIAM J. Discrete Math. 28 pp.[arXiv][journal]
Exact results for some extremal problems on expansions I, (with J. Song and L. Yuan), Commun. Math. Stat. 50 pp.[arXiv][journal]
A step towards a general density Corradi-Hajnal theorem, (with J. Hou, H. Li, L.-T. Yuan, and Y. Zhang) Canad. J. Math. 32 pp.[arXiv][journal]
Random Turan and counting results for general position sets over finite fields, (with Y. Chen, J. Nie, and J. Zeng) Sci. China Math. 28 pp.[arXiv][journal]
Hypergraphs with many extremal configurations, (with D. Mubayi and C. Reiher) Israel. J. Math., 34 pp.[arXiv][journal]
Finite hypergraph families with rich extremal Turan constructions via mixing patterns, (with O. Pikhurko) Forum of Math, Sigma, 13 (2025) Paper e53, 49 pp.[arXiv][journal]
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, 42 pp.[arXiv][journal]
Hypergraph anti-Ramsey theorems, (with J. Song), J. Graph Theory 108 (2025), no. 4, 808-816, 9 pp.[arXiv][journal]
A note on extremal constructions for the Erdos-Rademacher problem, (with O. Pikhurko), Combin. Probab. Comput. 34 (2025), no. 1, 52-62, 11 pp.[arXiv][journal]
Turan problems in pseudorandom graphs, (with D. Mubayi and David Munha Correia), Combin. Probab. Comput. 33 (2024), no. 5, 583-596, 14 pp.[arXiv][journal]
Cancellative hypergraphs and Steiner triple systems, J. Combin. Theory Ser. B 167 (2024), 303-337, 35 pp.[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, 10 pp.[arXiv][journal]
Stability theorems for some Kruskal-Katona type results, (with S. Mukherjee) European J. Combin. 110:103666, 2023, 20 pp.[arXiv][journal]
The feasible region of induced graphs, (with D. Mubayi and C. Reiher) J. Combin. Theory Ser. B 158 (2023), 105--135, 31 pp.[arXiv][journal]
A unified approach to hypergraph stability, (with D. Mubayi and C. Reiher) J. Combin. Theory Ser. B 158 (2023), 36--62, 27 pp.[arXiv][journal]
Tight query complexity bounds for learning graph partitions, (with S. Mukherjee) Conference on Learning Theory (COLT), 2022, 13 pp.[arXiv][journal]
Hypergraphs without non-trivial intersecting subgraphs, Combin. Probab. Comput. 31(6), 1076-1091, 2022, 16 pp.[arXiv][journal]
On explicit constructions of designs, (with D. Mubayi) Electron. J. Combin. 29 (2022), no. 1, Paper No. 1.53, 11 pp.[arXiv][journal]
Independent sets in hypergraphs omitting an intersection, (with T. Bohman and D. Mubayi) Random Structures Algorithms 61 (2022), no. 3, 493--519, 27 pp.[arXiv][journal]
On a generalized Erdos-Rademacher problem, (with D. Mubayi) J. Graph Theory 100 (2022), no. 1, 101--126, 26 pp.[arXiv][journal]
Sparse halves in K4-free graphs, (with J. Ma) J. Graph Theory 99 (2022), no. 1, 5-25, 21 pp.[arXiv][journal]
A hypergraph Turan problem with no stability, (with D. Mubayi) Combinatorica 42 (2022), no. 3, 433-462, 30 pp.[arXiv][journal]
Tight bounds for Katona's shadow intersection theorem, (with D. Mubayi) European J. Combin. 97:103391, 2021, 17 pp.[arXiv][journal]
The feasible region of hypergraphs, (with D. Mubayi) J. Combin. Theory Ser. B 148 (2021), 23--59, 37 pp.[arXiv][journal]
New short proofs to some stability theorems, European J. Combin. 96:103350, 2021, 8 pp.[arXiv][journal]
Structural results for conditionally intersecting families and some applications, Electron. J. Combin., 33(2), 2020, 13 pp.[arXiv][journal]
d-cluster-free sets with a given matching number, European J. Combin. 82:103000, 2019, 19 pp.[arXiv][journal]