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math.FA2025
High-low method and -adic Furstenberg set over the plane
Kevin Ren, Jiahe Shen
We establish a -adic analogue of a recent significant result of Ren-Wang (arXiv:2308.08819) on Furstenberg sets in the Euclidean plane. Building on the -adic version of the h…
math.PR2025
Triadic structures in multislice networks
Kevin Ren, Tara Trauthwein, Gesine Reinert
Networks provide a popular representation of complex data. Often, different types of relational measurements are taken on the same subjects. Such data can be represented as a \text…
math.CA2025
Incidence bounds related to circular Furstenberg sets
John Green, Terence L. J. Harris, Yumeng Ou +2
We prove bounds on approximate incidences between families of circles and families of points in the plane. As a consequence, we prove a lower bound for the dimension of circular $(…