# 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 (See this photo for our combinatorics group at SFU). My undergraduate studies were at University of Science and Technology of China, and my advisor was Jack Koolen.

My mathematical interests are mostly lie at the intersection of combinatorics, number theory, group theory, and harmonic analysis. My Erdõs number is 2

## Seminar

With Felix Clemen, we are organizing the Combinatorics Literature Seminar. Let us know if you are interested in giving a talk.

## Short CV

• 2018–Present   Ph.D. Candidate Department of Mathematics, University of Illinois at Urbana-Champaign, USA                                                                                      Supervisor:
• 2016–2018        M.Sc. Department of Mathematics, Simon Fraser University, Canada.                                                                                                                                         Supervisor: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:Thesis: Distance-regular graphs with bounded smallest eigenvalues.

## Selected Research Papers

(A complete list of papers is available here)

• Structures of sets with minimal measure growth in connected unimodular groups (with Chieu-Minh Tran), arXiv:2006.01824, preprint, 2020.                                                                                                                                                                                            Let $G$ be a connected unimodular group. Answering a question asked by Kemperman in 1964, we obtain classifications of $G$, $A$, and $B$ with $\mu_G(AB)=\mu_G(A)+\mu_G(B).$ When $G$ is compact, we also get a near equality version of the above result with explicit bound, this confirms conjectures asked by Griesmer and by Tao with assumption that $G$ is connected. As an application, we obtain a measure expansion gap result for connected compact simple Lie groups.
• The largest $(k,\ell)$-sum-free subsets (with Shukun Wu), arXiv:2001.05632, submitted, 2020.                                                                                                                                                                                                                                                                                                We determine the avoidance density of $(k,\ell)$-sum-free sets, this answers a question asked by Bajnok when the ambient abelian group is $\mathbb{Z}$. Generalizing a result by Bourgain for $(3,1)$-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 $N/(k+\ell)+\omega(N)$.
• Semialgebraic methods and generalized sum-product phenomena (with Souktik Roy and Chieu-Minh Tran), arXiv:1910.04904, submitted, 2019.                                                                                                                                                                                  Using tools from semialgebraic/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. This yields a structural result for symmetric non-expanders, resolving a question asked by de Zeeuw.
• Efficient polynomial time approximation scheme for the genus of dense graphs (with Bojan Mohar). [Extended Abstract] in 59th Annual IEEE Symposium on Foundations of Computer Science—FOCS 2018, 719–730, IEEE Computer Soc., Los Alamitos, CA, 2018.
• Efficient polynomial time approximation scheme for the genus of dense graphs (with Bojan Mohar). [Full Version] manuscript, available upon request, 2020.                                                                                                                                                                        We provide a Polynomial-Time Approximation Scheme 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.