Welcome to Xizhi Liu's Home Page

xizhi's photo Xizhi Liu

Email: xliu246@uic.edu

I am a graduate student in the Department of Mathematics, Statistics, and Computer Science (MSCS), at the University of Illinois at Chicago (UIC) (see here a photo of Chicago summer). My advisor is 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:

Combiatorics, extremal graph theory and extremal set theory.

Curriculum Vitae:



  • 2020 Spring, Math 165, Calculus for Business, (TA).
  • 2019 Fall, Math 110, College Algebra, (TA).
  • 2019 Spring, Math 310, Applied Linear Algebra, (Grader).
  • 2018 Fall, Math 310, Applied Linear Algebra, (Grader).
  • Research:


  • The feasible region of induced graphs, (with D. Mubayi and C. Reiher) (27 pages) Submitted.
  • A note on explicit constructions of designs, (with D. Mubayi) (9 pages) Submitted.
  • A unified approach to hypergraph stability, (with D. Mubayi and C. Reiher) (26 pages) Submitted.
  • Hypergraphs with many extremal configurations, (with D. Mubayi and C. Reiher) (32 pages) Submitted.
  • A note on hypergraphs without non-trivial intersecting subgraphs, (14 pages) Submitted.
  • Stability theorems for some Kruskal-Katona type results, (with S. Mukherjee) (20 pages) Submitted.
  • Cancellative hypergraphs and Steiner triple systems, (30 pages) Submitted.
  • Accepted

  • Independent sets in hypergraphs omitting an intersection, (with T. Bohman and D. Mubayi) (27 pages) Random Structures and Algorithm
  • On a generalized Erd\H{o}s-Rademacher problem, (with D. Mubayi) (21 pages) Journal of Graph Theory.
  • Sparse halves in K_4-free graphs, (with J. Ma) (19 pages) Journal of Graph Theory. Journal Version
  • A hypergraph Turan problem with no stability, (with D. Mubayi) (22 pages) Combinatorica.
  • Tight bounds for Katona's shadow intersection theorem, (with D. Mubayi) European J. Combin., 97:103391, 2021, (17 pages). Journal Version
  • The feasible region of hypergraphs, (with D. Mubayi) J. Combin. Theory Ser. B 148 (2021), 23--59. Journal Version
  • New short proofs to some stability theorems, European J. Combin., 96:103350, 2021, (8 pages). Journal Version
  • Structural results for conditionally intersecting families and some applications, Electron. J. Combin., 33(2), 2020, (13 pages). Journal Version
  • d-cluster-free sets with a given matching number , European J. Combin., 82:103000, 2019, (19 pages). Journal Version