# Yifan Jing

Email:  yifanjing17@gmail.com

Office:  1A Coble Hall, University of Illinois at Urbana-Champaign

Hi! I am a second year Ph.D. student in the mathematics department of University of Illinois at Urbana-Champaign, mentored by József Balogh and Xiaochun Li. Before coming to UIUC, I got my Master degree in Simon Fraser University (Canada) under the guidance of Bojan Mohar. My undergraduate studies were at University of Science and Technology of China, and my advisor was Jack Koolen.

My mathematical interests concentrate in Combinatorics, a branch of pure mathematics

My Erdõs number is 2.

## Short CV

• 2018–Present   Ph.D. Candidate Department of Mathematics, University of Illinois at Urbana-Champaign, USA

Supervisor:  József Balogh and Xiaochun Li

• 2016–2018        M.Sc. Department of Mathematics, Simon Fraser University, Canada.

Supervisor:  Bojan Mohar

Thesis:  The genus of generalized random and quasirandom graphs.

• 2012–2016         B.S. HUA-Loo Keng Talent Program in Mathematics (Honors Program), School of Mathematical Sciences, University of  Science and Technology of China, China.

Supervisor:  Jack Koolen

## Selected Research Papers

(A complete list of papers is available here)

• The largest $(k,\ell)$-sum-free subsets, arXiv:2001.05632, submitted, 2020. (See blog post by Sean Eberhard)                                                                                                                                                                                                                                                            We determine the avoidance density of $(k,\ell)$-sum-free sets. We also show that for infinitely many $(k,\ell)$, there is a function $\omega(N)\to\infty$ as $n\to\infty$ such that any set of $N$ positive integers contain a $(k,\ell)$-sum-free subset of size $N/(k+\ell)+\omega(N)$.
• O-minimal method and generalized sum-product phenomena (with Souktik Roy and Chieu-Minh Tran), arXiv:1910.04904, submitted, 2019.                                                                                                                                                                                                    Using tools from o-minimal geometry, we prove that for two bivariate polynomials  with coefficients in field with characteristic 0 to simultaneously exhibit small expansion, they must exploit the underlying additive or multiplicative structure of the field in nearly identical fashion.
• Efficient polynomial time approximation scheme for the genus of dense graphs (with Bojan Mohar). in 59th Annual IEEE Symposium on Foundations of Computer Science—FOCS 2018, 719–730, IEEE Computer Soc., Los Alamitos, CA, 2018.                                                                                                                                                                                    We provide a Polynomial-Time Approximation Scheme (PTAS) for approximating the genus (and non-orientable genus) of dense graphs. The running time of the algorithm is quadratic. We also extend the algorithm to output an embedding (rotation system), whose genus is arbitrarily close to the minimum genus. The expected running time of the second algorithm is also quadratic.
• The genus of complete 3-uniform hypergraphs (with Bojan Mohar).  J. Combin. Theory Ser. B.  (141) 223–239, 2020.                                                                                                                                                                                                                                                            In 1968, Ringel and Youngs confirmed the last open case of the Heawood Conjecture by determining the genus of every complete graph $K_n$. In this paper, we determine both the orientable and the non-orientable genus of $K_n^{(3)}$ when $n$ is even, generalizing Ringel–Youngs Theorems to hypergraphs. Moreover, it is shown that the number of non-isomorphic minimum genus embeddings of $K_n^{(3)}$ is at least $2^{\frac{1}{4}n^2\log n(1-o(1))}.$

## Teaching

• (TA) Math 482, Math 484, Math 213, Spring 2020, UIUC, USA.
• (TA) Math 482, Math 484, Fall 2019, UIUC, USA.
• (TA) Math 285, Math 482, Math 484, Spring 2019, UIUC, USA.
• (TA) Math 412, Math 482, Fall 2018, UIUC, USA.
• (TA) Calculus Workshop, Fall 2016, Spring 2017, Fall 2017, Spring 2018, Simon Fraser University, Canada.