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. 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 favor personal discussions as my primary mode of scholarly communication.
If you have any topic that would like to discuss with me, please feel free to reach out.
Furthermore, I sincerely request that you kindly exclude me from any seminar arrangements. Curriculum Vitae:
CV
Teaching:
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
A generalized Turan extension of the Deza-Erdos-Frankl Theorem, (with C. Helliar) (12pp) Submitted.
Faster coloring and embedding in dense hypergraphs via stability, (with J. Hou and H. Zhao) (21pp) Submitted.
A note on extremal constructions for the Erdos-Rademacher problem, (with O. Pikhurko) (13pp) Submitted.
Many vertex-disjoint even cycles of fixed length in a graph, (with J. Hou, C. Hu, H. Li, C. Yang, and Y. Zhang) (12pp) Submitted.
Toward a density Corradi-Hajnal theorem for degenerate hypergraphs, (with J. Hou, C. Hu, H. Li, C. Yang, and Y. Zhang) (37pp) Submitted.
Hypergraph anti-Ramsey theorems, (with J. Song) (14pp) Submitted.
Exact results for some extremal problems on expansions I, (with J. Song) (49pp) Submitted.
Random Turan and counting results for general position sets over finite fields, (with Y. Chen, J. Nie, and J. Zeng) (28pp) Submitted.
A step towards a general density Corradi-Hajnal Theorem, (with J. Hou, H. Li, L.-T. Yuan, and Y. Zhang) (32pp) Submitted.
Finite hypergraph families with rich extremal Turan
constructions via mixing patterns, (with O. Pikhurko) (57pp) Submitted.
Accepted
Turan problems in pseudorandom graphs, (with D. Mubayi and David Munha Correia) (17pp), Combin. Probab. Comput.
Hypergraphs with many extremal configurations, (with D. Mubayi and C. Reiher) Israel. J. Math. (34pp).
Cancellative hypergraphs and Steiner triple systems, J. Combin. Theory Ser. B 167 (2024), 303-337 (35pp).
Journal Version
Hypergraphs with infinitely many extremal constructions, (with J. Hou, H. Li, D. Mubayi, and Y. Zhang) Discrete Analysis 2023:18, 34 pp.
Journal Version
Hypergraph Turan densities can have arbitrarily large algebraic degree, (with O. Pikhurko) J. Combin. Theory Ser. B 161 (2023), 407-416 (10pp).
Journal Version
Stability theorems for some Kruskal-Katona type results, (with S. Mukherjee) European J. Combin. 110:103666, 2023, (20pp).
Journal Version
The feasible region of induced graphs, (with D. Mubayi and C. Reiher) J. Combin. Theory Ser. B 158 (2023), 105--135 (31pp).
Journal Version
A unified approach to hypergraph stability, (with D. Mubayi and C. Reiher) J. Combin. Theory Ser. B 158 (2023), 36--62 (27pp).
Journal Version
Tight query complexity bounds for learning graph partitions, (with S. Mukherjee) Conference on Learning Theory (COLT), 2022 (13pp).
Journal Version
Hypergraphs without non-trivial intersecting subgraphs, Combin. Probab. Comput. 31(6), 1076-1091, 2022 (16pp).
Journal Version
On explicit constructions of designs, (with D. Mubayi) Electron. J. Combin. 29 (2022), no. 1, Paper No. 1.53, (11pp).
Journal Version
Independent sets in hypergraphs omitting an intersection, (with T. Bohman and D. Mubayi) Random Structures Algorithms 61 (2022), no. 3, 493--519 (27pp).
Journal Version
On a generalized Erdos-Rademacher problem, (with D. Mubayi) J. Graph Theory 100 (2022), no. 1, 101--126 (26pp).
Journal Version
Sparse halves in K4-free graphs, (with J. Ma) J. Graph Theory 99 (2022), no. 1, 5–25 (21pp).
Journal Version
A hypergraph Turan problem with no stability, (with D. Mubayi) Combinatorica 42 (2022), no. 3, 433–462 (30pp).
Journal Version
Tight bounds for Katona's shadow intersection theorem, (with D. Mubayi)
European J. Combin., 97:103391, 2021, (17pp).
Journal Version
The feasible region of hypergraphs, (with D. Mubayi) J. Combin. Theory Ser. B 148 (2021), 23--59 (37pp).
Journal Version
New short proofs to some stability theorems,
European J. Combin., 96:103350, 2021, (8pp).
Journal Version
Structural results for conditionally intersecting families and some applications,
Electron. J. Combin., 33(2), 2020, (13pp).
Journal Version
d-cluster-free sets with a given matching number ,
European J. Combin., 82:103000, 2019, (19pp).
Journal Version
Thesis
Extremal Hypergraph Problems
(contains some unpublished results and short proofs to some published results).