Yifan Jing

Email:  yifan.jing (at) maths.ox.ac.uk

Office: N1.18, Andrew Wiles Building.

Hi! I am a Junior Research Fellow at Wolfson College, University of Oxford, and a Postdoctoral Research Associate at the Mathematical Institute at the University of Oxford, affiliated with the Number Theory Research Group. Starting in the fall of 2024, I will be an assistant professor at the Ohio State University.

I completed my Ph.D. degree at University of Illinois Urbana-Champaign in 2021, advised by József Balogh and Xiaochun Li (see here for our combinatorics group, and this photo for our harmonic analysis group). Before coming to UIUC, I got my Master’s degree in 2018 at Simon Fraser University (Canada) under the guidance of Bojan Mohar (See this photo for our combinatorics group). My undergraduate studies were at the University of Science and Technology of China, and my advisor was Jack Koolen. 

My Erdõs number is 2. Here is my CV (last updated Jul 2023). Click here for all my theses.

Research Interests

  • Arithmetic Combinatorics, Analytic and Combinatorial Group Theory, Lie groups, Abstract Harmonic Analysis, Representation Theory.
  • Additive and Combinatorial Number Theory, Analytic Theory of Numbers.
  • Applications of Model Theory, o-Minimality, NIP structures.
  • Combinatorial aspects of Harmonic Analysis over Euclidean space, including polynomial partitioning and Incidence Geometry.
  • Topological and Structural Graph Theory, Graphs on Surfaces, Extremal Combinatorics, Discrete Probability, Theoretical Computer Science.

Selected Research Papers

(A complete list of papers is available here)

  • Measure growth in compact semisimple Lie groups and the Kemperman inverse problem (with Chieu-Minh Tran), arXiv:2303.15628 (earlier version including non-compact case see arXiv:2006.01824v3), 50 pages, submitted, 2022.

    Let G be a compact semisimple Lie group and \mu a normalized Haar measure on G. We prove that for every measurable set A\in G, \mu(AA)\geq \min\{1,2\mu(A)+c\mu(A)|1-2\mu(A)|\}, where c is an absolute constant that does not depend on G. As an application, we obtain classifications of G, A, and B with \mu(AB)\leq \mu(A)+\mu(B) + \delta\min\{\mu(A),\mu(B)\}, this confirms conjectures asked by Griesmer and by Tao, and the case \delta=0 answers a question asked by Kemperman in 1964.

  • Measure doubling of small sets in SO(3,\mathbb{R}) (with Chieu-Minh Tran and Ruixiang Zhang), arXiv:2304.09619, 40 pages, submitted, 2023.

    We showed that for every \varepsilon>0 there is a \delta>0 such that if A \subseteq \mathrm{SO}(3,\mathbb{R}) is an open set with measure at most \delta, then \mu(AA)>(4-\varepsilon)\mu(A), where \mu is the normalized Haar measure on \mathrm{SO}(3,\mathbb{R}). This is sharp, and confirms a conjecture by Breuillard and Green.

  • A nonabelian Brunn–Minkowski inequality (with Chieu-Minh Tran and Ruixiang Zhang), Geometric and Functional Analysis, 33(4) 1048-1100, 2023.

    In 1953, Henstock and Macbeath asked whether there is a Brunn–Minkowski inequality in all locally compact groups. In this paper, we obtain such an inequality and prove it is sharp for helix-free groups (including linear algebraic groups, semisimple groups with a finite center, solvable groups, Nash groups, etc). This also answers questions asked by Hrushovski and by Tao.

  • On the small measure expansion phenomenon in connected noncompact nonabelian groups (with Jinpeng An, Chieu-Minh Tran, and Ruixiang Zhang), arXiv:2111.05236, 27 pages, submitted, 2021.

    We prove that a noncompact locally compact group G which admits small measure expansion pairs must be compactly homogeneous to a bounded dimension Lie group. The dimension bound we obtain is sharp. As an application, we complete the last open case of the inverse Kemperman problem.

Students

  • Albert Lopez Bruch
    Undergraduate summer research student, University of Oxford, Summer 2022 (co-advised with Akshat Mudgal)
  • Ahmed Ittihad Hasib
    Undergraduate summer research student, University of Oxford, Summer 2022 (co-advised with Akshat Mudgal)
  • Maria Matthis
    Undergraduate summer research student, University of Oxford, Summer 2022 (co-advised with Akshat Mudgal)
  • Anubhab Ghosal
    Undergraduate summer research student, University of Oxford, Summer 2023 (co-advised with Akshat Mudgal)
  • Ojas Mittal
    Undergraduate summer research student, University of Oxford, Summer 2023 (co-advised with Akshat Mudgal)