Welcome to Xizhi Liu's Home Page

xizhi's photo 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. degree 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. degree 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, Theoretical Computer Science, Complexity Theory.

Personal Statement:

I prefer personal discussions (online/in person) as my primary mode of scholarly communication. If you have any topics that would like to discuss with me, please do feel free to reach out. Additionally, I kindly request to be excluded from any seminar arrangements.

Curriculum Vitae:

CV

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

  • 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
  • Toward a density Corradi-Hajnal theorem for degenerate hypergraphs, (with J. Hou, C. Hu, H. Li, C. Yang, and Y. Zhang) 37pp. arXiv
  • Random Turan and counting results for general position sets over finite fields, (with Y. Chen, J. Nie, and J. Zeng) 28pp. arXiv
  • A step towards a general density Corradi-Hajnal Theorem, (with J. Hou, H. Li, L.-T. Yuan, and Y. Zhang) 32pp. arXiv
  • Finite hypergraph families with rich extremal Turan constructions via mixing patterns, (with O. Pikhurko) 60pp. arXiv

    • Accepted (free open-access journal, Chinese math journal)

  • Exact results for some extremal problems on expansions I, (with J. Song and L. Yuan) (50pp), Commun. Math. Stat., arXiv
  • Hypergraph anti-Ramsey theorems, (with J. Song) (14pp), J. Graph Theory. arXiv
  • Hypergraphs with many extremal configurations, (with D. Mubayi and C. Reiher) (34pp), Israel. J. Math., arXiv
  • A note on extremal constructions for the Erdos-Rademacher problem, (with O. Pikhurko) (13pp), Combin. Probab. Comput., arXiv, journal
  • Turan problems in pseudorandom graphs, (with D. Mubayi and David Munha Correia) (17pp), Combin. Probab. Comput., 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).