From the 1 of 6 linked papers with an AI index.
6 papers
Kakeya sets and dimension compression in compact Lie groups
Yifan Jing, Shukun Wu
We study two Kakeya set problems in compact semisimple Lie groups. In the first, motivated by the group structure, a Kakeya set is required to contain a left coset of every closed…
Computing Tools for Translation-Invariant Total Orders
Yifan Jing, Emma Yicheng Lou, Shaotian Sun +1
The paper presents TITO_Explore, a software library for representing translation‑invariant total orders (TITOs) and performing algorithmic operations such as canonical normalizatio…
A note on quantitative stability in Hilbert spaces
Yifan Jing
We study stability theory in Hilbert spaces quantitatively. We prove that the inner product on the unit ball is -stable for all , and it is not -stabl…
A structure theorem for sets with doubling
Yifan Jing, Akshat Mudgal
We prove a structural result for sets of integers with doubling at most , with sufficiently small. This generalises earlier work of Eberhard--Green--Manners which de…
Roth-type theorems in -free sets
Yifan Jing, Cosmin Pohoata, Max Wenqiang Xu
We show that for all integers , any -free subset of with size must contain a nontrivial solution to every fixed translation-invariant li…
A group-action Szemerédi-Trotter theorem and applications to orchard problems in all characteristics
Yifan Jing, Tingxiang Zou
We establish a group-action version of the Szemerédi-Trotter theorem over any field, extending Bourgain's result for the group . As an Elekes-Szabó-type applica…