Mukul Rai Choudhuri

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20242026

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math.CA2026

New bound on the Hausdorff dimension of Kakeya sets in $R^{4}$

Mukul Rai Choudhuri

We obtain a slight improvement to the trilinear bound of Guth-Zahl by application of Wang-Zahl's resolution of 3-D Kakeya to tubes inside a thickened neighborhood of a variety. Thi…

math.CA2025

A bound for plany Kakeya sets in $F_{q}^{4}$ using the planebrush method

Izabella Łaba, Mukul Rai Choudhuri, Joshua Zahl

Katz and Zahl used a planebrush argument to prove that Kakeya sets in $R^{4}$ have Hausdorff dimension at least 3.059. In the special case when the Kakeya set is plany, thei…

math.CA2024

An improved bound on the Hausdorff dimension of sticky Kakeya sets in $R^{4}$

Mukul Rai Choudhuri

Kakeya sets are compact subsets of $R^{n}$ that contain a unit line segment pointing in every direction. The Kakeya conjecture states that such sets must have Hausdorff dime…

New bound on the Hausdorff dimension of Kakeya sets in R4

A bound for plany Kakeya sets in Fq4​ using the planebrush method

An improved bound on the Hausdorff dimension of sticky Kakeya sets in R4

New bound on the Hausdorff dimension of Kakeya sets in $R^{4}$

A bound for plany Kakeya sets in $F_{q}^{4}$ using the planebrush method

An improved bound on the Hausdorff dimension of sticky Kakeya sets in $R^{4}$