Hong Wang - 2/3 Union of Tubes and Kakeya Sets @IhesFr

Uploaded November 2025 | Updated September 2026, 3 weeks ago

We discuss techniques (Cordoba argument, projection theory) to prove volume bounds on union of tubes in R2 and R3, with applications to the Kakeya problem.
This is joint work with Josh Zahl.

Hong Wang - 2/3 Union of Tubes and Kakeya Sets

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$Thomas Müller - Higher Dimensional Floorplans and Baxter $d$-permutations A 2-dimensional mosaic floorplan is a partition of a rectangle by other rectangles with no empty rooms. These partitions (considered up to some deformations) are known to be in bijection with Baxter permutations. A $d$-permutation is a $(d-1)$-tuple of permutations. Recently, in N. Bonichon and P.-J. Morel, J. Integer Sequences 25 (2022), Baxter $d$-permutations generalising the usual Baxter permutations were introduced. In this talk, I will introduce the $d$-floorplans which generalise the mosaic floorplans to arbitrary dimensions. Then, I will present the construction of their generating tree. The corresponding labels and rewriting rules appear to be significantly more involved in higher dimensions. Finally, I will present a bijection between the $2^{d-1}$-floorplans and $d$-permutations characterised by forbidden vincular patterns. Surprisingly, this set of $d$-permutations is strictly contained within the set of Baxter $d$-permutations. This is a joint work with Nicolas Bonichon and Adrian Tanasa (Université de bordeaux), this talk is based on arXiv:2504.01116. Thomas Müller (LIPN) Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.$

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Institut des Hautes Etudes Scientifiques (IHES) |

Hong Wang - 2/3 Union of Tubes and Kakeya Sets