# Welcome to Xizhi Liu's Home Page

**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).
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:**

CV

** Teaching:**

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: **

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.
Independent sets in hypergraphs omitting an intersection, (with T. Bohman and D. Mubayi) (27 pages) Submitted.
Sparse halves in K_4-free graphs, (with J. Ma) (19 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.
On a generalized Erd\H{o}s-Rademacher problem, (with D. Mubayi) (21 pages) Submitted.
Tight bounds for Katona's shadow intersection theorem, (with D. Mubayi) (20 pages) Submitted.
Cancellative hypergraphs and Steiner triple systems, (30 pages) Submitted.
A hypergraph Turan problem with no stability, (with D. Mubayi) (36 pages) Submitted.
The feasible region of hypergraphs, (with D. Mubayi) (37 pages) * 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